From e4ab872dd2f40983e1bce96904fe22624c3afe71 Mon Sep 17 00:00:00 2001 From: lcnature Date: Fri, 2 Sep 2016 10:12:26 -0400 Subject: [PATCH 01/30] a Changes to be committed: new file: brainiak/brsa/test.txt --- brainiak/brsa/test.txt | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 brainiak/brsa/test.txt diff --git a/brainiak/brsa/test.txt b/brainiak/brsa/test.txt new file mode 100644 index 000000000..e69de29bb From 06c869a431109610e47d20dcf8e151373aabf5bd Mon Sep 17 00:00:00 2001 From: lcnature Date: Fri, 2 Sep 2016 10:20:44 -0400 Subject: [PATCH 02/30] deleted: brsa/test.txt --- brainiak/brsa/test.txt | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 brainiak/brsa/test.txt diff --git a/brainiak/brsa/test.txt b/brainiak/brsa/test.txt deleted file mode 100644 index e69de29bb..000000000 From 64c4390818a2a40086ed68fa57e6f7da4ebca71b Mon Sep 17 00:00:00 2001 From: lcnature Date: Fri, 30 Sep 2016 09:06:41 -0400 Subject: [PATCH 03/30] changed some of the logging levels --- brainiak/reprsimil/brsa.py | 59 +++++++++++++++++++------------------- 1 file changed, 30 insertions(+), 29 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index c45b074b5..2de87d265 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -233,7 +233,7 @@ def fit(self, X, design, scan_onsets=None, coords=None, some visual datasets. """ - logger.debug('Running Bayesian RSA') + logger.info('Running Bayesian RSA') assert not self.GP_inten or (self.GP_inten and self.GP_space),\ 'You must speficiy GP_space to True'\ @@ -259,8 +259,8 @@ def fit(self, X, design, scan_onsets=None, coords=None, 'Design matrix and data do not '\ 'have the same number of time points.' if self.pad_DC: - logger.debug('Padding one more column of 1 to ' - 'the end of design matrix.') + logger.info('Padding one more column of 1 to ' + 'the end of design matrix.') design = np.concatenate((design, np.ones([design.shape[0], 1])), axis=1) assert self.rank is None or self.rank <= design.shape[1],\ @@ -273,7 +273,7 @@ def fit(self, X, design, scan_onsets=None, coords=None, # check the size of coords and inten if self.GP_space: - logger.debug('Fitting with Gaussian Process prior on log(SNR)') + logger.info('Fitting with Gaussian Process prior on log(SNR)') assert coords is not None and coords.shape[0] == X.shape[1],\ 'Spatial smoothness was requested by setting GP_space. '\ 'But the voxel number of coords does not match that of '\ @@ -386,8 +386,8 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): # of 0-99 are from the first scan, 100-199 are from the second, # 200-399 are from the third and 400-499 are from the fourth run_TRs = np.diff(np.append(scan_onsets, n_T)) - logger.debug('I infer that the number of volumes' - ' in each scan are: {}'.format(run_TRs)) + logger.info('I infer that the number of volumes' + ' in each scan are: {}'.format(run_TRs)) D_ele = map(self._D_gen, run_TRs) F_ele = map(self._F_gen, run_TRs) @@ -474,7 +474,7 @@ def _build_index_param(self, n_l, n_V, n_smooth): idx_param_fitV = {'log_SNR2': np.arange(n_V - 1), 'c_space': n_V - 1, 'c_inten': n_V, 'c_both': np.arange(n_V - 1, n_V - 1 + n_smooth)} - # for the likelihood functin when we fit V (reflected by SNR of + # for the likelihood function when we fit V (reflected by SNR of # each voxel) return idx_param_sing, idx_param_fitU, idx_param_fitV @@ -506,21 +506,22 @@ def _fit_RSA_UV(self, X, Y, # The rank of covariance matrix is specified idx_rank = np.where(l_idx[1] < rank) l_idx = (l_idx[0][idx_rank], l_idx[1][idx_rank]) - logger.debug('Using the rank specified by the user: ' - '{}'.format(rank)) + logger.info('Using the rank specified by the user: ' + '{}'.format(rank)) else: rank = n_C # if not specified, we assume you want to # estimate a full rank matrix - logger.debug('Please be aware that you did not specify the rank' - ' of covariance matrix you want to estimate.' - 'I will assume that the covariance matrix shared ' - 'among voxels is of full rank.' - 'Rank = {}'.format(rank)) - logger.debug('Please be aware that estimating a matrix of ' - 'high rank can be very slow.' - 'If you have a good reason to specify a lower rank ' - 'than the number of experiment conditions, do so.') + logger.warning('Please be aware that you did not specify the' + ' rank of covariance matrix to estimate.' + 'I will assume that the covariance matrix ' + 'shared among voxels is of full rank.' + 'Rank = {}'.format(rank)) + logger.warning('Please be aware that estimating a matrix of ' + 'high rank can be very slow.' + 'If you have a good reason to specify a rank ' + 'lower than the number of experiment conditions,' + ' do so.') n_l = np.size(l_idx[0]) # the number of parameters for L @@ -665,7 +666,7 @@ def _fit_RSA_UV(self, X, Y, / n_T)**0.5 t_finish = time.time() - logger.debug( + logger.info( 'total time of fitting: {} seconds'.format(t_finish - t_start)) if GP_space: est_space_smooth_r = np.exp(current_GP[0] / 2.0) @@ -705,8 +706,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, auto-correlation). The SNR is implicitly assumed to be 1 for all voxels. """ - logger.debug('Initial fitting assuming single parameter of ' - 'noise for all voxels') + logger.info('Initial fitting assuming single parameter of ' + 'noise for all voxels') beta_hat = np.linalg.lstsq(X, Y)[0] residual = Y - np.dot(X, beta_hat) # point estimates of betas and fitting residuals without assuming @@ -778,8 +779,8 @@ def _fit_diagV_noGP( requested. """ init_iter = self.init_iter - logger.debug('second fitting without GP prior' - ' for {} times'.format(init_iter)) + logger.info('second fitting without GP prior' + ' for {} times'.format(init_iter)) # Initial parameters param0_fitU = np.empty( @@ -820,10 +821,10 @@ def _fit_diagV_noGP( # something might be wrong -- could be that the data has # nothing to do with the design matrix. if np.any(np.logical_not(np.isfinite(current_logSNR2))): - logger.debug('Initial fitting: iteration {}'.format(it)) - logger.debug('current log(SNR^2): ' - '{}'.format(current_logSNR2)) - logger.debug('log(sigma^2) has non-finite number') + logger.warning('Initial fitting: iteration {}'.format(it)) + logger.warning('current log(SNR^2): ' + '{}'.format(current_logSNR2)) + logger.warning('log(sigma^2) has non-finite number') param0_fitV = res_fitV.x.copy() @@ -865,8 +866,8 @@ def _fit_diagV_GP( """ tol = self.tol n_iter = self.n_iter - logger.debug('Last step of fitting.' - ' for maximum {} times'.format(n_iter)) + logger.info('Last step of fitting.' + ' for maximum {} times'.format(n_iter)) # Initial parameters param0_fitU = np.empty( From 12476969a83c33890666be28cfd06900e9928d11 Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 2 Oct 2016 23:02:12 -0400 Subject: [PATCH 04/30] Creating new functions to prepare to a new version which explicitly deals with shared time series not explained by design matrix --- brainiak/reprsimil/brsa.py | 301 ++++++++++++------ ...tational_similarity_estimate_example.ipynb | 247 +++++++++++--- tests/reprsimil/test_brsa.py | 156 +++++++-- 3 files changed, 537 insertions(+), 167 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 2de87d265..7d5f5f555 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -365,7 +365,7 @@ def _F_gen(self, TR): else: return np.empty([0, 0]) - def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): + def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): """Prepares different forms of products of design matrix X and data Y, or between themselves. These products are reused a lot during fitting. So we pre-calculate them. Because of the fact that these are reused, @@ -379,6 +379,7 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): F = np.eye(n_T) F[0, 0] = 0 F[n_T - 1, n_T - 1] = 0 + n_run = 1 else: # Each value in the scan_onsets tells the index at which # a new scan starts. For example, if n_T = 500, and @@ -386,6 +387,9 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): # of 0-99 are from the first scan, 100-199 are from the second, # 200-399 are from the third and 400-499 are from the fourth run_TRs = np.diff(np.append(scan_onsets, n_T)) + run_TRs = np.delete(run_TRs, np.where(run_TRs == 0)) + n_run = run_TRs.size + # delete run length of 0 in case of duplication in scan_onsets. logger.info('I infer that the number of volumes' ' in each scan are: {}'.format(run_TRs)) @@ -400,22 +404,85 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): # D and F above are templates for constructing # the inverse of temporal covariance matrix of noise + XTY, XTDY, XTFY = self._make_templates(D, F, X, Y) + + YTY_diag = np.sum(Y * Y, axis=0) + YTDY_diag = np.sum(Y * np.dot(D, Y), axis=0) + YTFY_diag = np.sum(Y * np.dot(F, Y), axis=0) + + XTX, XTDX, XTFX = self._make_templates(D, F, X, X) + + X_base = [] + for r_l in run_TRs: + X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)) + res = np.linalg.lstsq(X_base.T, X) + if np.any(np.isclose(res[1], 0)): + raise ValueError('Your design matrix appears to have ' + 'included baseline time series.' + 'Either remove them, or indicates which' + ' columns in your design matrix are for ' + ' conditions of interest.') + if X0 is not None: + res0 = np.linalg.lstsq(X_base.T, X0) + if not np.any(np.isclose(res0[1], 0)): + # No columns in X0 can be explained by the + # baseline regressors. So we insert them. + X0 = np.insert(X0, 0, X_base.T, axis=1) + else: + logger.warning('Provided regressors for non-interesting ' + 'time series already include baseline. ' + 'No additional baseline is inserted.') + else: + # If a set of regressors for non-interested signals is not + # provided, then we simply include one baseline for each run. + X0 = X_base.T + logger.info('You did not provide time seres of no interest ' + 'such as DC component. One trivial regressor of' + ' DC component is included for further modeling.' + ' The final covariance matrix won''t ' + 'reflet them.') + X0TX0, X0TDX0, X0TFX0 = self._make_templates(D, F, X0, X0) + XTX0, XTDX0, XTFX0 = self._make_templates(D, F, X, X0) + X0TY, X0TDY, X0TFY = self._make_templates(D, F, X0, Y) + + return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, n_run + + def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): + return XTX - rho1 * XTDX + rho1**2 * XTFX + + def _make_sandwidge_grad(self, XTX, XTDX, XTFX, rho1): + return - XTDX + 2 * rho1 * XTFX + + def _make_templates(self, D, F, X, Y): XTY = np.dot(X.T, Y) XTDY = np.dot(np.dot(X.T, D), Y) XTFY = np.dot(np.dot(X.T, F), Y) - - YTY_diag = np.zeros([np.size(Y, axis=1)]) - YTDY_diag = np.zeros([np.size(Y, axis=1)]) - YTFY_diag = np.zeros([np.size(Y, axis=1)]) - for i_V in range(n_V): - YTY_diag[i_V] = np.dot(Y[:, i_V].T, Y[:, i_V]) - YTDY_diag[i_V] = np.dot(np.dot(Y[:, i_V].T, D), Y[:, i_V]) - YTFY_diag[i_V] = np.dot(np.dot(Y[:, i_V].T, F), Y[:, i_V]) - - XTX = np.dot(X.T, X) - XTDX = np.dot(np.dot(X.T, D), X) - XTFX = np.dot(np.dot(X.T, F), X) - return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX + return XTY, XTDY, XTFY + + def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, L, rho1): + # Calculate the sandwidge terms which put A between X, Y and X0 + # These terms are used a lot in the likelihood. But in the _fitV + # step, they only need to be calculated once, since A is fixed. + # In _fitU step, they need to be calculated at each iteration, + # because rho1 changes. + XTAY = self._make_sandwidge(XTY, XTDY, XTFY, rho1) + LTXTAY = np.dot(L.T, XTAY) + YTAY = self._make_sandwidge(YTY_diag, YTDY_diag, YTFY_diag, rho1) + XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + * XTDX[np.newaxis, :, :] \ + + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] + X0TAX0 = X0TX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + * X0TDX0[np.newaxis, :, :] \ + + rho1[:, np.newaxis, np.newaxis]**2 * X0TFX0[np.newaxis, :, :] + XTAX0 = XTX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + * XTDX0[np.newaxis, :, :] \ + + rho1[:, np.newaxis, np.newaxis]**2 * XTFX0[np.newaxis, :, :] + X0TAY = self._make_sandwidge(X0TY, X0TDY, X0TFY, rho1) + return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY def _calc_dist2_GP(self, coords=None, inten=None, GP_space=False, GP_inten=False): @@ -525,8 +592,10 @@ def _fit_RSA_UV(self, X, Y, n_l = np.size(l_idx[0]) # the number of parameters for L - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX = \ - self._prepare_data(X, Y, n_T, n_V, scan_onsets) + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, n_run \ + = self._prepare_data(X, Y, n_T, scan_onsets) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and # gradient. @@ -569,7 +638,7 @@ def _fit_RSA_UV(self, X, Y, self._initial_fit_singpara( XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, rank) current_logSNR2 = -current_logSigma2 norm_factor = np.mean(current_logSNR2) @@ -582,11 +651,13 @@ def _fit_RSA_UV(self, X, Y, if GP_space: current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 \ = self._fit_diagV_noGP( - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, rank) current_GP[0] = np.log(np.min( dist2[np.tril_indices_from(dist2, k=-1)])) @@ -616,11 +687,13 @@ def _fit_RSA_UV(self, X, Y, logger.debug('initial GP parameters:{}'.format(current_GP)) current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2,\ current_GP = self._fit_diagV_GP( - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank, + l_idx, n_C, n_T, n_V, n_l, n_run, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range) @@ -699,7 +772,7 @@ def _fit_RSA_UV(self, X, Y, def _initial_fit_singpara(self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, rank): + l_idx, n_C, n_T, n_V, n_l, n_run, rank): """ Perform initial fitting of a simplified model, which assumes that all voxels share exactly the same temporal covariance matrix for their noise (the same noise variance and @@ -756,7 +829,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, res = scipy.optimize.minimize( self._loglike_AR1_singpara, param0, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, rank), + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, options={'disp': self.verbose}) current_vec_U_chlsk_l_AR1 = res.x[idx_param_sing['Cholesky']] @@ -769,11 +843,13 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, return current_vec_U_chlsk_l_AR1, current_a1, log_sigma2 def _fit_diagV_noGP( - self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank): + l_idx, n_C, n_T, n_V, n_l, n_run, rank): """ (optional) second step of fitting, full model but without GP prior on log(SNR). This is only used when GP is requested. @@ -794,14 +870,24 @@ def _fit_diagV_noGP( param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() + L = np.zeros((n_C, rank)) tol = self.tol * 5 for it in range(0, init_iter): # fit V, reflected in the log(SNR^2) of each voxel + rho1 = np.arctan(current_a1) * 2 / np.pi + L[l_idx] = current_vec_U_chlsk_l_AR1 + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, + X0TY, X0TDY, X0TFY, L, rho1) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, - args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, - current_a1, l_idx, n_C, n_T, n_V, + args=(XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + LTXTAY, current_vec_U_chlsk_l_AR1, + current_a1, l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, rank, False, False), method=self.optimizer, jac=True, tol=tol, @@ -836,7 +922,7 @@ def _fit_diagV_noGP( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, - n_T, n_V, idx_param_fitU, rank), + n_T, n_V, n_run, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 3}) @@ -855,11 +941,13 @@ def _fit_diagV_noGP( return current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 def _fit_diagV_GP( - self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank, GP_space, GP_inten, + l_idx, n_C, n_T, n_V, n_l, n_run, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range): """ Last step of fitting. If GP is not requested, it will still fit. @@ -881,6 +969,7 @@ def _fit_diagV_GP( param0_fitU[idx_param_fitU['a1']] = current_a1.copy() param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() + L = np.zeros((n_C, rank)) if self.GP_space: param0_fitV[idx_param_fitV['c_both']] = current_GP.copy() # param0_fitV[idx_param_fitV['c_space']] = \ @@ -890,12 +979,20 @@ def _fit_diagV_GP( # current_GP[1] for it in range(0, n_iter): # fit V - + rho1 = np.arctan(current_a1) * 2 / np.pi + L[l_idx] = current_vec_U_chlsk_l_AR1 + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, + X0TY, X0TDY, X0TFY, L, rho1) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=( - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, - XTDY, XTFY, current_vec_U_chlsk_l_AR1, current_a1, - l_idx, n_C, n_T, n_V, idx_param_fitV, rank, + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + current_vec_U_chlsk_l_AR1, current_a1, + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range), method=self.optimizer, jac=True, @@ -927,7 +1024,7 @@ def _fit_diagV_GP( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, n_T, n_V, - idx_param_fitU, rank), + n_run, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, @@ -963,7 +1060,7 @@ def _fit_diagV_GP( def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - log_SNR2, l_idx, n_C, n_T, n_V, + log_SNR2, l_idx, n_C, n_T, n_V, n_run, idx_param_fitU, rank): # This function calculates the log likelihood of data given cholesky # decomposition of U and AR(1) parameters of noise as free parameters. @@ -995,8 +1092,6 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # Such parametrization avoids the need of boundaries # for parameters. - LL = 0.0 # log likelihood - # n_l = np.size(l_idx[0]) # the number of parameters in the index of lower-triangular matrix # This indexing allows for parametrizing only @@ -1012,10 +1107,6 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # each element of SNR2 is the ratio of the diagonal element on V # to the variance of the fresh noise in that voxel - # derivatives - deriv_L = np.zeros(np.shape(L)) - deriv_a1 = np.zeros(np.shape(rho1)) - YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag # dimension: space, # A/sigma2 is the inverse of noise covariance matrix in each voxel. @@ -1028,10 +1119,16 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # dimension: feature*space LTXTAY = np.dot(L.T, XTAY) # dimension: rank*space - LAMBDA_i = np.zeros([n_V, rank, rank]) - for i_v in range(n_V): - LAMBDA_i[i_v, :, :] = np.eye(rank) \ - + np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) * SNR2[i_v] + # LAMBDA_i = np.zeros([n_V, rank, rank]) + # for i_v in range(n_V): + # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L)\ + # * SNR2[i_v] + # LAMBDA_i += np.eye(rank) + # LTXTAXL = np.empty([n_V, rank, rank]) + # for i_v in range(n_V): + # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) + LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) + LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank LAMBDA = np.linalg.inv(LAMBDA_i) # dimension: space*rank*rank @@ -1045,35 +1142,42 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) # dimension: space*feature (feature can be larger than rank) - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) \ + # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) \ + # / n_T + sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ / n_T # dimension: space, LL = -np.sum(np.log(sigma2)) * n_T * 0.5 \ - + np.sum(np.log(1 - rho1**2)) * 0.5 \ + + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ - n_T / 2.0 + # log likelihood XTAXL = np.dot(XTAX, L) # dimension: space*feature*rank - deriv_L = -np.einsum('ijk,ikl,i', XTAXL, LAMBDA, SNR2) - \ - np.einsum('ijk,ik,il,i', XTAXL, YTAXL_LAMBDA, YTAXL_LAMBDA, - SNR2**2 / sigma2) \ + deriv_L = -np.einsum('ijk,ikl,i', XTAXL, LAMBDA, SNR2) \ + - np.dot(np.einsum('ijk,ik->ji', XTAXL, YTAXL_LAMBDA) * SNR2**2 + / sigma2, YTAXL_LAMBDA) \ + np.dot(XTAY / sigma2 * SNR2, YTAXL_LAMBDA) + # - np.einsum('ijk,ik,il,i', XTAXL, YTAXL_LAMBDA, YTAXL_LAMBDA, + # SNR2**2 / sigma2) \ # dimension: feature*rank dXTAX_drho1 = -XTDX + 2 * rho1[:, np.newaxis, np.newaxis] * XTFX # dimension: space*feature*feature - # because this term will be used twice below, we explicitly name - # it here. + dXTAY_drho1 = -XTDY + 2 * rho1 * XTFY + # dimension: feature*space + dYTAY_drho1 = -YTDY_diag + 2 * rho1 * YTFY_diag + # dimension: space, deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) * \ - (-rho1 / (1 - rho1**2) - + (-n_run * rho1 / (1 - rho1**2) - np.einsum('...ij,...ji', np.dot(LAMBDA, L.T), np.dot(dXTAX_drho1, L)) * SNR2 / 2.0 - + np.sum((-XTDY + 2.0 * rho1 * XTFY) - * YTAXL_LAMBDA_LT.T, axis=0) / sigma2 * SNR2 + + np.sum(dXTAY_drho1 * YTAXL_LAMBDA_LT.T, axis=0) + / sigma2 * SNR2 - np.einsum('...i,...ij,...j', YTAXL_LAMBDA_LT, dXTAX_drho1, YTAXL_LAMBDA_LT) / sigma2 / 2.0 * (SNR2**2.0) - - (-YTDY_diag + 2.0 * rho1 * YTFY_diag) / (sigma2 * 2.0)) + - dYTAY_drho1 / (sigma2 * 2.0)) # dimension: space, deriv = np.zeros(np.size(param)) @@ -1082,10 +1186,11 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, return -LL, -deriv - def _loglike_AR1_diagV_fitV(self, param, XTX, XTDX, XTFX, YTY_diag, - YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - L_l, a1, l_idx, n_C, n_T, n_V, idx_param_fitV, - rank=None, GP_space=False, GP_inten=False, + def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, + X0TAX0, XTAX0, X0TAY, LTXTAY, + L_l, a1, l_idx, n_C, n_T, n_V, n_run, + idx_param_fitV, rank=None, + GP_space=False, GP_inten=False, dist2=None, inten_dist2=None, space_smooth_range=None, inten_smooth_range=None): @@ -1134,47 +1239,55 @@ def _loglike_AR1_diagV_fitV(self, param, XTX, XTDX, XTFX, YTY_diag, # due to the constraint. But I have not reproduced this often. SNR2 = np.exp(log_SNR2) # If requested, a GP prior is imposed on log(SNR). - deriv_log_SNR2 = np.zeros(np.shape(SNR2)) - # Partial derivative of log likelihood over log(SNR^2) - # dimension: space, rho1 = 2.0 / np.pi * np.arctan(a1) # AR(1) coefficient, dimension: space - YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag + # YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag # dimension: space, - XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ - * XTDX[np.newaxis, :, :] \ - + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] + # XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + # * XTDX[np.newaxis, :, :] \ + # + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] # dimension: space*feature*feature - XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY + # XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY # dimension: feature*space LTXTAY = np.dot(L.T, XTAY) # dimension: rank*space - LAMBDA_i = np.zeros([n_V, rank, rank]) - for i_v in range(n_V): - LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) \ - * SNR2[i_v] - LAMBDA_i += np.eye(rank) + # LAMBDA_i = np.zeros([n_V, rank, rank]) + # for i_v in range(n_V): + # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) \ + # * SNR2[i_v] + # LAMBDA_i += np.eye(rank) + # LTXTAXL = np.empty([n_V, rank, rank]) + # for i_v in range(n_V): + # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) + LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) + LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) + # dimension: space*rank*rank LAMBDA = np.linalg.inv(LAMBDA_i) # dimension: space*rank*rank YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) # dimension: space*rank - YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) + # YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) # dimension: space*feature - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1))\ + # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1))\ + # / n_T + sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ / n_T # dimension: space LL = -np.sum(np.log(sigma2)) * n_T * 0.5\ - + np.sum(np.log(1 - rho1**2)) * 0.5\ + + np.sum(np.log(1 - rho1**2)) * n_run * 0.5\ - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 - n_T * 0.5 # Log likelihood of data given parameters, without the GP prior. deriv_log_SNR2 = (-rank + np.trace(LAMBDA, axis1=1, axis2=2)) * 0.5\ + YTAY / (sigma2 * 2.0) - n_T * 0.5 \ - - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA_LT, - XTAX, YTAXL_LAMBDA_LT)\ + - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA, + LTXTAXL, YTAXL_LAMBDA)\ / (sigma2 * 2.0) * (SNR2**2) - + # - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA_LT, + # XTAX, YTAXL_LAMBDA_LT)\ + # Partial derivative of log likelihood over log(SNR^2) + # dimension: space, if GP_space: # Imposing GP prior on log(SNR) at least over # spatial coordinates @@ -1291,14 +1404,14 @@ def _loglike_AR1_diagV_fitV(self, param, XTX, XTDX, XTFX, YTY_diag, def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - l_idx, n_C, n_T, n_V, rank=None): + l_idx, n_C, n_T, n_V, n_run, + idx_param_sing, rank=None): # In this version, we assume that beta is independent # between voxels and noise is also independent. # singpara version uses single parameter of sigma^2 and rho1 # to all voxels. This serves as the initial fitting to get # an estimate of L and sigma^2 and rho1. The SNR is inherently # assumed to be 1. - LL = 0.0 n_l = np.size(l_idx[0]) # the number of parameters in the index of lower-triangular matrix @@ -1308,16 +1421,16 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, - np.sqrt(n_C**2 * 4 + n_C * 4 + 1 - 8 * n_l)) / 2) L = np.zeros([n_C, rank]) - L[l_idx] = param[0:n_l] + L[l_idx] = param[idx_param_sing['Cholesky']] - log_sigma2 = param[n_l] + log_sigma2 = param[idx_param_sing['log_sigma2']] sigma2 = np.exp(log_sigma2) - a1 = param[n_l + 1] + a1 = param[idx_param_sing['a1']] rho1 = 2.0 / np.pi * np.arctan(a1) XTAX = XTX - rho1 * XTDX + rho1**2 * XTFX LAMBDA_i = np.eye(rank) +\ - np.dot(np.dot(np.transpose(L), XTAX), L) / sigma2 + np.dot(np.dot(L.T, XTAX), L) / sigma2 XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY LTXTAY = np.dot(L.T, XTAY) @@ -1327,7 +1440,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, LAMBDA_LTXTAY = np.linalg.solve(LAMBDA_i, LTXTAY) L_LAMBDA_LTXTAY = np.dot(L, LAMBDA_LTXTAY) - LL = LL + np.sum(LTXTAY * LAMBDA_LTXTAY) / (sigma2**2 * 2.0) \ + LL = np.sum(LTXTAY * LAMBDA_LTXTAY) / (sigma2**2 * 2.0) \ - np.sum(YTAY) / (sigma2 * 2.0) deriv_L = np.dot(XTAY, LAMBDA_LTXTAY.T) / sigma2**2 \ @@ -1340,7 +1453,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, * L_LAMBDA_LTXTAY) / (sigma2**3 * 2.0) deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) \ - * (-rho1 / (1 - rho1**2) + * (-n_run * rho1 / (1 - rho1**2) + np.sum((-XTDY + 2 * rho1 * XTFY) * L_LAMBDA_LTXTAY) / (sigma2**2) - np.sum(np.dot((-XTDX + 2 * rho1 * XTFX), L_LAMBDA_LTXTAY) @@ -1348,7 +1461,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, - np.sum(-YTDY_diag + 2 * rho1 * YTFY_diag) / (sigma2 * 2.0)) LL = LL + np.size(YTY_diag) * (-log_sigma2 * n_T * 0.5 - + np.log(1 - rho1**2) * 0.5 + + np.log(1 - rho1**2) * n_run * 0.5 - np.log(np.linalg.det(LAMBDA_i)) * 0.5) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index a53817b9d..aa96a5f06 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false }, @@ -44,7 +44,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false }, @@ -80,17 +80,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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2bTF48GCcPn0aM2bMwIEDB0o9Bu7fvx979+5FVFQUqlWrhosXL2LGjBkICQnBiRMn/tZT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\nSUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "design = utils.ReadDesign(fname=\"example_design.1D\")\n", "\n", - "\n", - "design.design_used = np.tile(design.design_used[:,0:17],[2,1])\n", - "design.n_TR = design.n_TR * 2\n", + "n_run = 2\n", + "design.design_used = np.tile(design.design_used[:,1:17],[n_run,1])\n", + "design.n_TR = design.n_TR * n_run\n", "\n", "\n", "fig = plt.figure(num=None, figsize=(12, 3), dpi=150, facecolor='w', edgecolor='k')\n", @@ -122,11 +133,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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PwohPZnR0mKvhqSLdPDD5uT6eNHd2uk+gE91x8zNge3lmJpCeHvsAt3Ah8N57\nCSla0tDRQc8oKys5pFtdhFFJ92670f+70+QiHojSHb/SHe/v3cB1s6PDm9Tz5G/cuMQp3bvvTm6o\nICSlt9jLOZY4kaFT9fVUj3RLd7JJt9r/2Y2dmzcD338ffjm8wGOwX6W7sDB8e3lLC7W/nqZ0l5UB\nBQW02NQdkCzSLUp3aiCkW4HYy7sP+BmFoXRzBzdgAMV1pwJBlG51MuNWdxO9UMFlZJU1EqF7FuvE\nuaGheyTAUcH3csSI5MR0q89OtZcXF9P9F9Lde9CV7eVqyIPXRLG0FEhLA8aMSSzpBoKpOKmwl7e2\nmv1oshb7m5qIHCfyuTstHKSSdNuNJW1tycu94Qa/Snd5OTnI+vcPn3Sz6NTcHG4uG16ES9Y8u6KC\nnjsv7nV12GUv95OPp60NOPFEYOlSf+cRpTs16JGku70dOOYYYMUK+7/bDTaGIUp3d0KY9nIe2KZO\nBb79NjWJJlpbSTX2Q5DVgdit7iY6plu3lwM0QYhl4tzRQYNwdyPdPNkcMSK5Snd2tlXpHjAgvgWP\n7gY30t3SAqxdm9zypALxkuZkZC9Xz+OE7dspZjU/P/5EahxqM3IkvfcbftDebrqbkkm61etNptKt\nviYCTnHpqYzpthvnWluT72Swg1/SvXMnMGgQ/T/sLcN4/guES4iTrXTztXSXRIWxKt1vvQW8/DLw\n4Yfe5zAMUbpThR5Jujdvpgq4bFn03xobyWrywQfWz2tqzEFXSHfXR5ikm4991FH0+umniT+HF9ra\naBLKqoQbUqV0J5J083MMi3R/+63/FeAg4Mnm8OFU9rD31uRnN2SIVenOzSXS3RuVbl2V+fe/gSlT\nkl+mZCMRSnefPuEr3X5I99ChFIddXx9f1mmenLLS7XdCqfahySRl6n1K1ryD+5Bkke7Bg+3/Fga8\nSHd3U7qbmih0CQhf6WanJ2C9d+3tiVW+kx3TzfUunvp3zDHA/ffH/vvFi4E77/T3Xa4TdmKKW31Z\nuJBe/Sj6auiNKN3JRY8l3YD95L+ykjrm776zfs4dTlaWkO7ugGQo3RMmELlJhcW8tZVIN+A9MPtV\nuhO9ZZge0w3ETvzCJt233QZcdVXij6uSbiB8lYzvT3GxVenOySHi3dtId3Nz9DWXldFzCHsBJNVI\nBOnOzU3MfXrzTeCss8z3QezlTLo5EaNXH+BGAHgiP2IEvfpVuvl32dnJVbrVOUoy7eXqa7wwDHfS\nXVxs/7dmZzxzAAAgAElEQVQw4JVIrbWVPk+16qkSK7ds6s3NlCsFSC7pVuvGHnsAzzyTuPNwf9PW\nlpxM8olQupcujS+/z4IFwGOP+ftuLEp3czPwwgv0fz8hV0zMc3NF6U42eiTpLimhVzvSzYODaqUB\nzA5n2LDErMC99hpw2WXxH0dgj2Qo3f36AT/8IfDJJ4k/hxdaW2kLHcD7GtXJTDLt5XpMNxC70s3t\nMizS3dgYzoquTrrDVlH42emkuzcq3UVF9H99ksH3JewsvKlGIrKX5+bGby+vrgbOPZcmlmpm/UjE\nPI8bSktpcdPP7gdHHQXccYfz3/me5OdTewhKuouKeo+9PFFKo7ondqpJd22tqQzbjSV8j1Otdqv3\n3u05qKQ7iL188WJgzpxgZVLnxFxHOjqATZsSG66j9jfJULvjJd1tbVSP162LvQzbtvlf5LIj3V6C\nyWuvUd3fd19/SjePmfvuK6Q72eh1pJs/U1f1ALPDGTYsMYPDO+8AixbFfxyBPbgjDWNirZLJ8eNp\n0Ek2VKXbi4iqnbOXvTwS6Z328ubmcEg3Xysra2FbU+2UbtVebnfvm5q6xt60iYRb3C7fg+6WHyAo\n4lG6DYPaRE5O/Er3b39rTvR4HK2vN2NR/drL/ZDur7923+6Kz9WvH7URvxNK/l1xsdjLg8LtGlJB\nuocMof872cu5XKmE2ibcnkOsSverrwLz5gWzhdsp3XwPE7kQpfY3yYjrjtdezjl94iHd27fHR7q9\nlO6FC4FJk4Bp04Ip3fvuK/byZKNHkm43e7kfpTsRg8POnT1faUklEql0t7TYZ1nt25fi0fS6kgxw\nTDfgXY/8KN28nVheXuJJt2ovj9XiHLbSzc840ZZjXelOFulWY7rZXu6kdB9+OE3AehJU0t3ble5Y\n6jRP4uK1l7/3HvDww8AvfkHvua+sq6NtjgD3ySYn9FFJt1Mytc5OOv769c7H43uSmUmqtV+lm39X\nXJwae3leXve1l/sl3YlU8p99FnjooejPa2up3jklIe2KSndQ0u2HSDc20r3YuNF/mSoqTHcK3zse\nb8Ii3d1B6WZuUFERu5MsFqXbb/byhgbgpZeAn/2M5gVOSvfOnWbdKS2l/nb0aFG6k40eSbpjUbor\nKsyJayI6gqoqf0mwBLEhkaT7jjuAY48136tKd0EBTSqSHeefaKWbv8PJ2RIBO6U71gzayVC6AfsF\nlDVrKNFaLOAJ57Bh9Bo26eYBuaiIzs3xlE72csMgdTDI5CsZaGuLj+yxvbxfPyHdsdxHbg/x2stv\nuw046CDghhvovap0FxRYz2WHnTup/JxIDXDuP6qraTxdt86ZeCRC6a6tTd64zf3HoEHdN3u5F+nm\nxZdEjqFPPw38/e/Rn9fW0gJGVpa70t1dSTfgr73ytTvt4GOHykpqh2qZwiDdavmD1EHDAG6/Pfiz\nSxTpBtwX/JxQV0f3MSyl+6236Denn07Pr7Iy+lp5G8UXX6T37C4qLKT72dPzn3QlhEq6P/zwQ8yc\nORPDhg1DWloaFi9eHObpdiFWe3lBQeK2ZWBLiuz5HQ4SSbq3brUqIrrSDSRX7TYMa0w3d8KdnfaT\nQT9Kt0q6e2NMN7dDOyvV738PXHxxbMetr6c9VAcOJJUg7MlcQwOdLy+P6klNjWkTtnMZVFTQc+pq\nsd5XXQWcf37sv29poXo3ZIgz6e7p9vJ4tgzj3+bkOPcrfrBxI3DEESbBtlO63cZAVmX82Mu57dbV\nRY/fDD5XUKVbJd2dnfFvXeYXdXWkyiZT6U6WvdwwiHQPHEhjaSKvr7HR3kZbW0uLj06km8esMBdH\nGxtpu1G3hU713vsl3TzO6vextZUyY6shRHztK1f6LjYqKswwqUTYy//2N/tnFKvSvW0bcP31wCuv\nBCtHvPZyta+JxWK+bRu9NjX5dykA9qTb7n6VlFD7GjPGXDSxC7lqaDCTAnMeDc6L4tSfChKPUEl3\nQ0MDfvCDH+D+++9HhH0rSUCs9vJEkm6efPd0tSVV4M4nERPr+nprZ6aSyVSQ7o4O6pz1RGqXXmpP\nDv1kL+fPBw4MXicbG+1XeLtbTDdgP7hUVgKrVsW2LUp9PRGXtDSaOCdD6c7KMgmKmoXUzmWwZQu9\nJtMy6wfr15uLo7HAD+nu6X1vopTuWI9hGLRgOWwYLeZFIlal24+9nOuvn0RqfhQn1V4eROnm33E8\ncLLaC7tUEjXvWLoU+P579+8kS+luajLDpBK9x3RjIxELfbGopsYk3XZjSTKU7k2baEvar792/k48\nSreuYn7xBXDNNVaCHYvSXVFhhknFay+vrASuvBJ46qnov8Ua083fDerailfprqykvi0nJz7SDfhr\nA42NNJ/wm0itrIz6ukjE7L90izk/zy+/NP8+dKhJuiWuO3kIlXQfd9xxuOWWW3DSSSfBSORGfy6o\nqaF/TpN/N3s5k+5EqNOsdPf0iV+qkMg9p3XSnWqlmwcl3V7+9df2A7mffbp1e3mQ5vjww2Qh1X/j\ntmVY0ObOE7ewQjLclO6aGuoXYiGBTLoBurdMuisqwiHgDQ20rRETFB7QnezlTLq7mtLNK++xorcr\n3ZyjAYhtMqmT7lgs5jU11P8OG0ZqbX6+Oe75tZerSndWFk02/ZBup8mvai8vKiLS7ac/UZVuvrZk\ngPuPRG0HdcklwM03u38n0dnLnUg3939hke6Ojuhx2a/SHSbp5rrjRaYZ8ZJunSCrnwW1l/P+9vHa\ny3lRzC4Jbaykm+9ZUNId7y4PFRU0D9xjj9hIt0qA1ev9z3/snQCNjVSH/drLmXQDptLtRro5j8aQ\nIebCqMR1Jw89LqabVe699nJXuqurrRONykpqWJmZiVW6k5GdsTfCzl7+7LPAqacGP1ZDg/WZ6zHd\nQHJJN58/L49eucMsK7O3S/qxl6tb6RhGsDpeVkbXzwROL6eudLe3B29DdhOGRMKNdPPk0E2ZcIIT\n6T7zTFIfEg0npVtNpKYueGzdSq9dTemuq3N+zjfeSP/c0FuU7i1bgBNOiF5AUNtXvPbyWI/BCz67\n7UavatLJujpy1aSnu5O7sjLq5zIzTTXJydrNbXfQIG/SzUp3R4c/gqVuGQYkL7s1b/eXCFJqGLS1\nk9eWQcmyl+ukO5Ex63wNetvnmO7s7NTFdIdFup3s5TpB5v8PHEjtxK/zrKKC2nIkkjjSbUeQ29vN\nfifIwk+qlG4W5MaMiS2mW1W61Wd91lnA449Hf7+xkdqM30RqKukuKKCFS71d8O+qqkhcEKU7deix\npHvvvd2VbsBclQcSay9vazMHou428Wttpa0HXn011SVxhx3p/vxz4M03gx+LE6UxWVEV3Px86sSS\nGfPCg0N2NpCRYV5jWRl1prqK7CeRmkq6gWD1kuvyN99EH7NPH7o/DD/b/thBnzAkGnz9ds8xUaR7\n4EAa1Do6gM8+87d1R1C4Kd25uVQ31PvXVZXu2lrnOvjMM8D777v/XiXd3WHLsPZ24MEHg2/dtnQp\n9cWrVlk/j5d08+/jId28oMNJBJl0c3K/nBzKP+BGKqqqzK3FuDxuSvegQcC4cf7s5Tyh9KPicL8Z\nxF7+2WfWstbWUhxrEJePqnTHO++orKTyuMWxd3R4bz8UFOo9cCLdYcR0A/akO9Ux3X5Id1OTuZ94\nvEq3HelubAQOOYT+72dca22l51hQYG2zYZDutjZz/EqG0s2/iyemu6AAGDs2cUo395F295VJd0eH\nOV74VbrT0+n/Tko3AHz6KdX/oUNpLtG/vyjdyUSXJN2zZ8/GzJkzLf8WLFjg67clJVTxxo93V7oB\n6wQ8kaRbXUXtbqT7nXcoNujll1NdEnfYke6aGnq+QSeQXCe4Y1MV3LQ0IlOpsJdnZJgr9g0N9NrS\nEt1R871IT/dOpKYnZ/MDvj96hu+WFqu1HDAH06AkT22XYZAlJ6Wbk5EB0cTGD+yU7tWrzS1bEo2G\nBveYbsDa73VV0u2kdDc00P3zUqKYdBcXW2M7DaNrKt1ffAH88pf0GgR8H3SSmSil24+9fNs2eyLH\npFtXupubabKYk0OEwU3Nqq42FwK5PG6ku7DQffKr2suzs+n/fuqBumUYl8sNHR20J+6//mV+9sYb\nFMfqN3kbYG73lwglmOuI2/n9KqxBUF9v9j3JtJcDVtLd2Un304l0c64UoGso3TwWh2UvnzyZFsX9\nWMx5fsOkm4/Jr3V1wRYM/ZLuWJTuTZuChaAFtZc3NFhdfWwvHzuW+EXQ/nbbNvMZqqEd6tyD0dlJ\nf2OXI5/Lr9INEJl2It3p6cBrr9H/eYGxqKj3Kt0LFiyI4pqzZ88O9Zx9Qj16jJg3bx4OOOCAmH5b\nUmImduEtddQcbnV1NEnYts3saAzDtJdzbFVnp1XBC4LuTLqffZZeg04Okw3VMtTeToMLd2DqNiV+\nwISvudk6OcjIoNeCgtTYy/v2pYljQ4N1IlVaap2otrZSXc3O9mcvB4JNuHgSbKd0q9ZywJ74+YGX\n0n377cCMGUCM3YJjIrX6emrreXmJsZdv3w4sW0bvwyC6jY1WpVu3l/N5ObYrWYnUSkqAq68GFiyI\nrhM6mBhz+1Lx9df0d9WFpKOzkyYjnOiQYzsLC03CB3QtpVudMLIC5QdMXHSSqSq6YSdSu+wyOv9X\nX1mf2dat5kI1QM9iwwazP83NTTzpZpvne++5X1e/fuZE18/EvrmZ+tDcXOtY4oTS0ugFUK5vQTKf\nq4nU4m2jXEcqK+l52rUvv1mzg4BJNy8KM5JNurneMOnW+1+VdHUF0p2fT20oDHt5YyOR+gkT/JFu\nHhcHD6Z7Z3fM2lpzocAL69dT/auqMt0HjHiV7rY2GvfYYeP3d35J9513ku177Vp6X1EB7Lcfke6O\nDhrrxo71X+7t26nP+vbb6Kzweh3lv3Of2NpKz99J6TaMaNJtF3LF51NdrDxHKCzsvUr3rFmzMGvW\nLMtny5cvx+TJk0M7Z5dUuuPB5s207UFuLk3OdNJbXw+MGkX/546mpoYakzqBiGfVWZ0wdifS3d4O\nvPACNcKvvkrevqGxQB149G0tgg6oPElSV0T79jUXa9RYxWRAJd28Yq+Sbl3JYMXZLQmgmkgNSIzS\n3doaTbBitZfX10dna1dx223mHpNB0d5uEjF9RZfrzA9/CPz3v8ETSnFMJmAq3WGSbla6s7Opftop\n3ep5t26l+tvaGu6WRB9/DDz/vHc8KUDlaGujOqhbcXmC6Ea6VScKr9bzJEO99q7U9/K9D5qsj/sy\nJ9KdkxNfIjU/9vLSUmr7d91l/XzbNlPlBsx+ktu+H3t5ENK9Y4dp89y2zf643BempTmTFDswuYlE\nqDxeBJjD2OxyUQQl3Ymyl6tuCCflSm0TiSTdrNbrpDsjg+pAMmK6ue07Kd1cxwcPTr29vLmZypiZ\nmXh7uWGYuT8mTQpGup3s5ep1+cH69cChh9L/9WRq7e10jj59YlO6gWAW86D28g0bqPz8fd5OeMwY\neh/UYr5tm/lbr63Y+HOVdKtl1+tKXR1dn1+l+4c/NAm2KN2pQehbhq1YsQJfffUVAGD9+vVYsWIF\nNvOIFQJKSigDo9Pkv66OSLm6vYna4QQZqJ3QXZXujz6ie3HDDdTYY7HbJgstLeZKvh53pN7/H/8Y\n+Mtf3I/Fv1c7Z9U2PXhwamK63ZRu/fus7PjZMgyInXSrJMlO6Y4npptjMHXS3d5OZYh1osTPdfDg\n6MGFj3n44XQf16xxP1Z7OyVJ4wUIu5ju5cvpfZhKNyed2raNLGP9+kVb+w2DyMHee9P7MNVuHsj9\nEA61buiTrv8bKtDU5J2fwI50q8fuSkp3vKRbt5erSnXYSndVFU2Sb77Zarvk7cIYTLrDVLrZXg7Q\n5NjuurhPCqp08/f9bP3H90HtR7m+Ben71ERq8ZLSdevMa3eymIeldNslg+NnG4kkNqa7vd28V3ak\n2ymRGv+mqChcpZvrjldMd2am+6KUYcRmL29ro0XmrCxSaFet8rZj6/byeEh3Wxv1c0cdRe91gtzW\nRoTba8FBh9qO7bKiOyGovZzz5nBfzQ6b3Xencgcl3du3m32Wfl/1OYIT6XZSurmd+yXdvBDSp4+5\nM09vVrpTgVBJ99KlS7H//vtj8uTJiEQiuOaaa3DAAQfgpptuCu2cfkh3fj5NkJlIqdaaIAO1E1SV\npjtlL3/2Wdqn8eKLqVF2ZYt5S4vZabiR7mXLgCefdD5OR4fZIamds0omnZRutrkmGmpMN+83WlZG\n6k1mZjTpjkXpDlIv6+tpoaq21ozjVM+rwk5t9XsOHjh0sqSGDcQCfq4jRkQvnqikG/C2mG/YADz9\nNPDWW2a5VXt5VRVtyzFqVGxbp3mBE6kB1Mdt20avkUi0tb+2lr6/117m+7DAixlBSbc+MV6xwlwY\ncpoYq6RbT5bFx45EutaCp1/S/eCDVkeJH6U77Jju6mrgV7+i7/761+bndqR7506znsUS0+2WvVxN\naATYT35bWswxPMhYri4g5uX5V7rVOhaP0p0I+/X69cCUKfR/pySO3O97ZZUPAjelm59tIu3l6jXE\nonQXF3cNe7lOupubqZ1xH9bWRuOHbi93Urr1OOysLKoP9fXAz35GSRlVLF0KXHopjREVFTS/yMuz\nxnQ3NNBcUL0uL5SU0Nzo0EOpzHakmx0QQeogh4AMGhSb0u2XdDOR3bCBflNbS/1Onz7AyJHBSHdd\nHd1/nXT7Vbq9YrrtSDcnF1UXWhob6X5zeN6QIWb4rCjdyUWopHvq1Kno7OxER0eH5d+jjz4ayvk6\nO2kFmu3lQDTp5lVZlUipq3yJUrpZeexKEz873HEHcNhhZN19/nnacisrC9hnn65NutVEJE6km2P1\nv/zSeSVPfT5OSrdTTPecObSdT6KhK91sLy8ooFVMJ6XbbWITT/byujrg4IPp/2pct53SzSpsIpVu\nfq6xKrX8XJl0q0SYj7nHHjRweZHu1avplQd9nXS3ttJn06cTkfEzqaipoWv34yxh2yBA521sNPs6\nXelmNY5JdzKUbj/qskr+1e93dhLpnjqV3jtZzFXSnZVFr+pWVQCt3qdS6T7pJOCf/zTf+yXdv/kN\nxcUzuC/T7dSJIN1paTQRA5yPYRhUhpEjgZtuoszy/Fy2bo22l7e3mxn12V6eKKWb7eVDhtDYapfB\n3E8MrB3U3/mxl3PbsrOXB+n7ErlP97p1ppLlpHRzGQcNCt9eXlUVLukeOdKddOvtX1W6OaQwDMRK\nur/5Brj3Xpqv8HeAaKXbK6ZbJd3TpwMPPEDiw4EHAscfT26iZ58FjjwSeOghCinkZGFpadEx3UEy\n+gNmu9xjD3pGTqQ7qNLd1ET3a/ToYKSb75ff+sdtZ+NGKzcAiDwH2TaM+0Ine7lTTDcnUotV6W5r\niw5zzcqinR+ys81nCojSnWz0qJjusjKqbF5Kd04ONSI7pTsRpHvnThrU1BXDrop336UO+eSTaRLF\n+1wfeGDXJt0tLeZWM06ku7bWVHCcthKz22PUr9K9Zg2wZEli1MxHHzUnEE728uJiM1uzCl4k8GMv\njzWme599qD6rKpxdTDfbnmOJ6ebkd/pkidXoeO3lw4dT/6AOdGqyn3339Sbd331Hr2xv00k3Y9o0\nevWjLpeWEqFgQu8GXekGzPPzwgufk10JyVC6Y7WXq/Vw/Xq6vunT6b0f0h2JWPtyPvaQIante5cv\nj16gAtxtkU1NpurEqKqyt1Pz8eKxl2dmmiE6TseorydyMnCg+VyWL6d+tawsWukGzGtkezlPFOvr\ngYMOMhMUAf5Jd0uLuaVRWhpNYu0Up2TZy+2U7lgSqSVqn+7mZmrvEyfSs/Kylw8enJyY7jBIN9/z\nMWOspJvHfyelWyXdQHj9IZfDrd41N9N4qpJu/p0e7hbUXq6S7kiEEiF+/z2wcCG1mf33B376U+An\nP6HF9PnzzbhlwFqmxkZzYS0I6U5Pp0XuUaOiCXJ7e+xKd2am/TG9fgf4W9Tq7LQq3So3AJz7HSew\nzTvemG5+1e9XWRkp8GqCOz3kio+blUV95/7701yIwYtQXTmHU09CtyHdO3d6WyBYRXAj3arSzQ1q\n40ZT5fYzUG/e7J7op6qKGoHTXpF+0N4O/P3vwbZGiAXl5cC55xL5/sMfTJvtgQfSpLErxUWq0El3\nR4c52WHSzc83PR14/XX746gTJLeYbt5/WQVn5ozXmtPaClx4ITkNgGh7eWMjPafiYvvMlKrSHVYi\ntbw8yoSqEwndXg5Q+wo6oWlooMlS//6Jt5erpBuwPi9O9pOZSQsLXmqzqnR3dlJZ1ZhugAbYkSPp\n/37uAz8LP9fHidSAaIWb/68q3ZEIPTe/ZYkViSDdHM8dhHQD1kUxPnZxcWr7rpYWa1vkMldVOS9I\n8TWo9bOqyrQMq5O9RCjdKul2speri1LjxlH9WrbMtC+6kW7dXl5SQgu5nPOgpYUmoX5IN98bXphz\n2jZMtZf36UOTTD9kT/2dH3u5XUx3UHu5up95vKR00yY63pgx9guzDJ70DxyYfNKdqEm9Srp37jTP\nyf1bbq63vRwIz2Lud59uXenm33G5ud2wG8VvIjWVdDPS0ykXyTffAA8/TEkRFyygud8bb1ASUW6/\nur188GDqJ4KQ7t13p9/YEeRYY7pZ6Q6TdFdVmX2hndK9227BtgRkpXv4cLofdjHdqmjjlkgtJyf6\nfpWXE2lWd1rirORqXLfqkHv0UeCvfzX/xn2qWMyTg25Dun/5S+Cii9y/w6vPTvZydZBTLcMrV1LC\nCcCf0n3mmWQtdsLOnfGT7o8+ohXKWLYxCgImc9OmUQK19HT6/MADaVLFVqeuBjWmW98TWSfdxxxD\nA4udIq1OzN2UbrZZquD3Xsm3vMDH4bripnTbke4gSndWFg14fgc7lVjuvbdV6bazlwP+Jq06WMHl\n61XBE/947eVMulUlsabGTPaz3370LEeOJIuznq0dMEn3pk10Dw0jWumePNk9tn3lSqtFTXdq6OBt\ntAAzkRpgT7oHDDD7vC1baEDmCUNXsZe7ke4hQ8xFAj8x3YA96S4sTK3S3dJibYvq/53yiPKkR1e6\n99qL2rYT6Y41e3lmphmv6UTc+RkMHEgTuwMOoFhQdlHYke6NG+nZ6GoW1z911xDAH+nme8N1ecwY\nZ3u52id5xZTb/S5ITHc89vKmJupfc3Pjt5dz3Rg71p10J9NerpLuRCZS42sYPZpeue+praV7ydtn\n8v1l6Eq3X9K9eTMwc2Z09n4nxGov10k3fx50yzB+5XFCRUYGzaOvuoru0+mn09j3xhv2SjePy0HG\n9PXrTWXXzV4ej9IdZK/uIPZybjfjxlmVbr43PNb4dTdu305tIzc32kEA0L1Q74Gb0p2fb28vV63l\ngKl0O5HucePM5wNE50URhItuQ7q/+MJcNXJCeblptbCLLeUtanJzrZbEFSuCke6SEvds1lVVNKjF\nQ7qZWCUq2YkdDMNcKdOx997UwekW87Vrw0keFhTNzValWx0QeDDlifhZZ1HntHJl9HH8KN3c4eoW\ncz7P99/Hdg36cbhDddoyLF6lOyPDjNnyWy95AM/Npcn/N9+YA46dvRywL6MX6uudSXeilO4RI+hV\nV7p5gDvzTHKXnHUWbYFltxfw6tU0aFVWmteok+4DDoiOr1Zx8cXArbea792U7pISsr1/9BE5LXir\nGSDaXg4Q6VaV7uHD6Rn17dt1lG6nbb1WrAB+8AOqpzk5/pVudQGVw4dyclKrdLe22ivdgHNcN48p\nev0cNCiaZCZC6WZiDPgj3QCp7irp1mO6AZoQc51U1Sxux3x9dqSbn5s+odYnvwUF9qRJtYnz+YPa\ny3nrPye0t9OEtk8fb3t5ba0zuePvJULpXr+e2vhuu/lTuoPYy08/ndQxJ6TSXg5YtwvkxU7uI9Vn\nz3Wc5zt+xpNFi2hu+NJLznvD64iVdHN5nOzl3FZjUbqdUFAAHHccjencfvWY7nhI96hR1uSKgGkv\nV/uG1lZS21XMm2fNi8HugFGj6Pt+5xhBlG4+5iGHmKQ7Pd2MsS4ooPL7HUvVbRXtSDdgPx7aKd15\nef5Id//+9F07e7kdROlOLroF6a6tpQbg1UlWVlLHEYnYx5by/9VEanV1tEo8aRL9zYt0M1F1m1yq\nSnesq8ncYMLcW7e2lo5vR7ozMij2QyXdDQ1kwX322fDK5BfcCUUiVtI9aJBZT3iidtJJ1BHZWcz9\nxnQDzqQ7mUp3cTHVP3VSyoqzl9LN1xSEdKsTw733pjrDi19OSvduu3kvkKkwDFNN91K6Ywm34HvC\nqpxOanhAzcoCLrkEuP12GojsMp2XlwPHHkvv2WrPBKO4mBSRk092V7o3bbJOYPh67fo3njyvWWP2\nJV5Kt066gdjcB1u3+iMsTU1m3xqvvZz74UGDgtnL1Zju3Fz7LYOSBcOwV7rZBuhFuvm1qYl+N3Bg\ndCxhomO6/djLASLdGzdSGEZGhkmCAXPf4Y0braTbSenmY3P74+sBovsA/g1PELOz7euaahMH/JM9\nPabbra2UltIC2Jgx3vbyX/0KOPts6+8XLKC6rfat8SrB69aR8pue7k2609Kon/AzNyktJeLJoR92\ncCLdKglOFelW61FQpXvZMlpwOPpoIqZ+iJZhJE7p1kl3JEJtLkhMtx+cdRa9hqF0jxpFr2ouC1Xp\n5vMsWEAOMXV8f+454D//Md9zHDwf06/FPAjp5nZzyCE01peUmAnmAPMe+d1Cdvt20+7tRLrV+8qf\ncz3mDPatrfQM2tutfbUd6Qaitw1zI91FRTTupnULNtj90S1uM1usvTpJTmDG0K1q/H+2l1dVmYMJ\nK91eMd3V1dQQ3CaXrHTHk0gtGaSb1Sk70g1QQ1Tt7d9/T+UJEtMSFlpa6P5yllLuuEaNstrLc3Ko\nA5s2zZt0u8V08/EYqt08XtLN5II7ZDWmOzub/l5TYyrdHR3WBQB1yzCn+tLaal6T296gOtQ2s+ee\n9F5DqLMAACAASURBVH++XqeY7qCkm23aXko3h4cEhbo9Un6+vb1ch+qEYbC1fMYMeuW2wQQjI4N2\nAZgwwZl0t7ZS+7GzpdpNavizkhLzN25KtxrTrW7ppJJxvzjsMOD++72/py5i+LWX67kFWlpokYCt\n5YMGxW4v55jOVCnd7e3mHruMlhaq28OGOSdT4/pWWUmTT77+/PzoGGY+dnZ2fKQ7iL0cMOPLFy+m\ndq5P1AYNMvOmAFYLqb4YqhN6wBoWtnEjtSeA6ljfvmZdd1LEY7WX6zHdDQ3OCxEczz1+vLe9fMsW\nK2GtrCSS88gjVhGAY55jTcqpEp3iYmcVkCfffq29r71Gr27fdSLdaihMGKR75Eiqf3ytNTXRpFud\nf3EdLyggAqv2Lzt3Ul4VdTfb664jd9fChRSj7CdsoLGRxueCAm/SHTSRGmB/H+NRugFaKM7PN/OQ\nqPNWfoZ+SXdVFbVrnXSrBFmN6eZr3LLFXGRUr0ttX9xncTn9ku6g9vL+/cldBpCrh+d/gLMA4wQn\npVu9Ll3p7t/fuj0c11tenFTrlRPpHjLEP+nu35/6qB/9yN81CeJDtyDdnNyoutp9UGKlm6GTbp6w\ns73cMID336fVYc7w66V0+7FRJiKRGjeYZJBuu0YLUCbU7783E4gx6YjHpnrPPbTtTLxgldWLdPPK\n5JQp9tmh/SjdvJCjdrRqVt8wle6sLPN+M+kGrJMqP/byeJXu3FzzPvC9dlK6eZXV7wSSByAvpVv/\nv1/wPenXj5QyJ6VbhV3Geq4/U6cSwdaVbhVs3dXbCtty1Wt0U7pV0s3PLEhMNyvdQUl3Rwf9Xs2Y\n7QTuR9LT/dvLWbHUt05hcjdwYOyJ1FKtdKuWQAa3ld13d1a6uV52dFBdUAnv2LH0LJhk8vEyMsLN\nXl5dTfeSvzd2LLWXZcus8dwMHn/92Mu9SPfttwNnnEHPkfvySMR6fJ3Y6PbyIEo31ycujxPJ4Hju\nPff0VrpramjizW2SLbSffx5tLwdiD91at87Mcl9cTO3BbtGAk1H5XXh99VV6dVvMbWuLJt3sXuKJ\nfhiJ1HJzqR9RlW7VtaR+l8sKUP0YMMBsX6+/Tg6+hQuBW24hK/2bbwJvvQXcdhsRRL/JQbnOFBcn\nLpGaWp/tYv+dSDcnYPNCdjbtysE5k3RymJXln3RzCAzXxSFDqMxeSjf33+o9a262Pj+uu+xUDaJ0\n2zkE7MAklvMFLF1qdfPEonQ72cu5L9OV7qwsa9I8LncQ0l1YaL9lmCD16JKkW5+scyyumqHaDpWV\n/pVunhy88w4Nnn739uQJptOqp2GYinsiYrpTqXRPmEDn586NSUfQ7aAYS5YAV18NPPmk+/cMw91G\nzPbNfv3MybUd6Va3wXCy+tfX03HS052V7r59aZBWSRif48ADiXTrdfbRRykbvB/oSjd3sn36WJOh\nFBWZHaxKuv0kUlOV7ljt5awi8L12iunebTcarP3WEz6Hm9LNilwsycDUyYuuYAdVuocPp/swYkS0\n0q0iErESYAarZGo/5hbTbad0+7GXNzZSvYrVXl5dTW3QT9wc9yMjRvi3l+flWdVodY9dIJi9vKCA\nrpdt7qlWurl8utLdrx+pNF72coCIqU66W1vNRZt4STcru172cnWvZYDq9eTJ9H81npvB4yrXSS97\neSQSnX0foOf41lt0zR99RL/hhRrAbAN6fdPt5bHEdPPk1qm9bNlCE+jhw71jurlNc94PTs742WdW\npdtpD2Y/MIxopdsw7GM0g5Du9nZKsOVWLqe49OZm070EJD6RWiRC51Pzh6j2cj6vndKdkUFtqrqa\nSMuJJ1Lo1OrVlG/jl78ELr+cnD4zZ9Jv7PpyO3CdGTIk8fZywJ50q6o0v/bta46ZflBcbPYF8cR0\nL1tGr1wX09Kik6mpMd18jdwnqG3VSekG7BO0OS2KtLTQ8/Mb0z1kCAkHGRnU/6mk28716Ibt202h\nRCfd3J/pSrdOuvXtXtVj1Nfbk259kV1Id9dBlyTdeuNZudIk025K186dwZRuAPjkEzOOEPC2l7O1\n2mly2dREDSVepTsZpLusjDpFdaFCBVs9eW/ieJTutjaKlzUMb7XyySfJuueE9nYiBEy6WenOyKDO\nUlW67ZKDqOBBRZ0wqASVoSufTAgOOoiesWqnNgxaIectwLygK928EhyJWEk3x3QD8SndQcIe1IUq\nPSGXm70cMO/Jhg3U5pxUUz9KNydBC0Pp9ku6v/vOtNiPGmW2CzvSDdiry3ZZj92yl/P1+rWXDxhA\natpxx9F7L6Vb3cteBdd1P6Sb7+fo0f7t5fq2PvGQbtXypyrdevbiZMHOzuhH6a6oMNXjigor6eZJ\nLFvMVdIddvZydQ9YwLSY+1G67bKXq0p3Xp7Vos6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p5u/q9vKwlG4n0q3vHKRCn0+rSndb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\n9ttv47DDDnP9bWHhPAwatBjAYsyfvxiLFy/GrFmzLErQpk00ELByaGf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I6C4tSlJ0n3km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\n008fesyyLDz99NOO/RNCMujv7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "noise_bot = 0.5\n", "noise_top = 1.5\n", @@ -177,7 +199,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -202,11 +224,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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ffr47Z/FqIWl9ijmw4bzUZLLF7/sp201aqxhJh5MWkWpK7qAraVs2LpUHaW3V3YDHIuJB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\nSqzzQuDKiPh5iXUeAvxe0ux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axHxYOOiOUENZ09br4VrZPL1gZlYiZy+YmVlbPNI1s8oraj3d4eCga2aVV+R6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\nctA1MyuRg66ZWYkcdM3MSuSga2ZWov8P+445MMAlm/MAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# ideal covariance matrix\n", "ideal_cov = np.zeros([n_C,n_C])\n", @@ -219,8 +262,8 @@ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_cov)\n", "plt.colorbar()\n", - "plt.xlim([0,17])\n", - "plt.ylim([0,17])\n", + "plt.xlim([0,16])\n", + "plt.ylim([0,16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal covariance matrix')\n", @@ -231,8 +274,8 @@ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_corr)\n", "plt.colorbar()\n", - "plt.xlim([0,17])\n", - "plt.ylim([0,17])\n", + "plt.xlim([0,16])\n", + "plt.ylim([0,16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal correlation matrix')\n", @@ -248,11 +291,42 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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AEBAQAJ7nMX78eHTs2FHnYKcsOTg4AACePn2KmjVrit57+vSp1oH1ClNPl2Zn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FvONxWB0IxUOGd33Pp9vTrYxn4/mAEH0Qc9QzcgYjU1mjQzehHjWHUdmKUKjPou7aXMhRD8aC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\n9u3bTVZW1pT3k5KSzM6dO/2fDw4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gQQYAV18NfOc7wK5d3rZH8Ad791JlcqNVy0RUivYj0YS+64V6Vxf9/7Zt9NjI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\n0TvqeXn2awyJUBe0iFCPE23oe0kJXYx6V0+b6+y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kCGnDkSIJ9WRy1K2E+u7dobm6ZkJd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AewfAv1QYPIJcxVqLuVZ+vtpZDMQnDUUyngy18G/u3fjMRydvvUc80SW1MTXjK5fDjqhw8HdzYu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\nQm9vr+v/3nnnnRg1ahRqampw4YUXoqWlJ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "\n", @@ -348,13 +422,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "scan onsets: [ 0. 186.]\n" + ] + } + ], "source": [ - "scan_onsets = np.linspace(0,design.n_TR,num=3)[:-1]\n", + "scan_onsets = np.linspace(0,design.n_TR,num=n_run+1)[:-1]\n", "print('scan onsets: {}'.format(scan_onsets))" ] }, @@ -367,11 +449,25 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "BRSA(GP_inten=True, GP_space=True, epsilon=0.0001, init_iter=20,\n", + " inten_smooth_range=None, n_iter=50, optimizer='BFGS', pad_DC=False,\n", + " rand_seed=0, rank=None, space_smooth_range=None, tau_range=10,\n", + " tol=0.002, verbose=False)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "brsa = BRSA(GP_space=True,GP_inten=True,tau_range=10)\n", "# Initiate an instance, telling it that we want to impose Gaussian Process prior over both space and intensity.\n", @@ -391,14 +487,35 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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XqH9yzFcIoTE/E+t9lDBbPddCxpgCF7M4L2I13GVmDybG/wJwDbBt4jF/Z0KM6Y7UmP5K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\ntjE0deYcc3HtS0j94jiOUx9taHNu2sx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7AFsDT7dWNeecc41oumulkcnYJb0bOA3YHbgyTwWdc877yLO1vY88BvdzgVPM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\nIHfOuQ73/wHFGIT2j2SJawAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(brsa.C_[1:, 1:], vmin=-0.1, vmax=1)\n", + "plt.pcolor(brsa.C_, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", "plt.ylim([0, 16])\n", "plt.colorbar()\n", @@ -410,8 +527,8 @@ "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(brsa.U_)\n", - "plt.xlim([0, 17])\n", - "plt.ylim([0, 17])\n", + "plt.xlim([0, 16])\n", + "plt.ylim([0, 16])\n", "plt.colorbar()\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", @@ -429,17 +546,38 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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f63/F89kT928F9MXvpifKLWU1r2SYz47H/i/CYkz7ADdH3XePx/mLeK3dT3iCeH+ifTdh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\nKT5idhyn8PjMP8dxnILRaTP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dC/tpnZ+tlf2sYllSQ3RtYBFwE7BDRHS9wdnH03yY2cDoUVdGRPyhUcqI2Lfm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\nZjOzknFgNjMrGQdmM7OScWA2MyuZ/w9Ad/Bd4e6ZhQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "betas_point = np.linalg.lstsq(design.design_used, Y)[0]\n", "point_corr = np.corrcoef(betas_point)\n", "point_cov = np.cov(betas_point) \n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(point_corr[1:, 1:], vmin=-0.1, vmax=1)\n", + "plt.pcolor(point_corr, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", "plt.ylim([0, 16])\n", "plt.colorbar()\n", @@ -450,7 +588,7 @@ "plt.show()\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(point_cov[1:, 1:])\n", + "plt.pcolor(point_cov)\n", "plt.xlim([0, 16])\n", "plt.ylim([0, 16])\n", "plt.colorbar()\n", @@ -470,11 +608,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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1u9T+4xh+vfNtrL1+9XCG/45p2AaySNpf0s8lPSlpQNK7ql7/frG98nF1bjtm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\nMDEz/tLMb8MvKvGR8Td54Rv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Z8TXq4AUMLZOMzMysHx38nVGL5kgzMxtOPDIyM2sXHTwycjIyM2sXXk1nZmY2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\n4y/7zUIXdu7XZw+7Km+Hbc/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig = plt.figure(num=None, figsize=(5, 5), dpi=100)\n", "plt.pcolor(np.reshape(brsa.nSNR_, [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", @@ -495,14 +654,26 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RMS error of Bayesian RSA: 0.13665981702261623\n", + "RMS error of standard RSA: 0.1433569522028947\n", + "Recovered spatial smoothness length scale: 5.595133988654466, vs. true value: 3.0\n", + "Recovered intensity smoothness length scale: 4.611783121422689, vs. true value: 4.0\n", + "Recovered standard deviation of GP prior: 0.184521447350508, vs. true value: 0.8\n" + ] + } + ], "source": [ - "RMS_BRSA = np.mean((brsa.C_[1:,1:] - ideal_corr[1:,1:])**2)**0.5\n", - "RMS_RSA = np.mean((point_corr[1:,1:] - ideal_corr[1:,1:])**2)**0.5\n", + "RMS_BRSA = np.mean((brsa.C_ - ideal_corr)**2)**0.5\n", + "RMS_RSA = np.mean((point_corr - ideal_corr)**2)**0.5\n", "print('RMS error of Bayesian RSA: {}'.format(RMS_BRSA))\n", "print('RMS error of standard RSA: {}'.format(RMS_RSA))\n", "print('Recovered spatial smoothness length scale: {}, vs. true value: {}'.format(brsa.lGPspace_, smooth_width))\n", diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index fad358938..a1aea8799 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -40,8 +40,10 @@ def test_fit(): file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") # Load an example design matrix design = utils.ReadDesign(fname=file_path) + + # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,0:17],[4,1]) + design.design_used = np.tile(design.design_used[:,1:17],[4,1]) design.n_TR = design.n_TR * 4 # start simulating some data @@ -112,6 +114,13 @@ def test_fit(): # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) + # We also test that it can detect baseline regressor included in the design matrix for task conditions + wrong_design = np.insert(design.design_used, 0, 1, axis=1) + with pytest.raises(ValueError) as excinfo: + brsa.fit(X=Y, design=wrong_design, scan_onsets=scan_onsets, + coords=coords, inten=inten) + assert 'Your design matrix appears to have included baseline time series.' in str(excinfo.value) + # Now we fit with the correct design matrix. brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, coords=coords, inten=inten) @@ -167,13 +176,15 @@ def test_gradient(): import numpy as np import os.path import numdifftools as nd + np.random.seed(100) file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") # Load an example design matrix design = utils.ReadDesign(fname=file_path) + n_run = 4 # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,0:17],[4,1]) - design.n_TR = design.n_TR * 4 + design.design_used = np.tile(design.design_used[:,1:17],[n_run,1]) + design.n_TR = design.n_TR * n_run # start simulating some data n_V = 200 @@ -237,36 +248,96 @@ def test_gradient(): Y = signal + noise - scan_onsets = np.linspace(0,design.n_TR,num=5) + scan_onsets = np.linspace(0,design.n_TR,num=n_run+1) # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) # test if the gradients are correct - XTY,XTDY,XTFY,YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX = brsa._prepare_data(design.design_used,Y,n_T,n_V,scan_onsets) + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, n_run_returned =\ + brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) + assert n_run_returned == n_run, 'There is mistake in counting number of runs' + assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ + 'Dimension of XTY etc. returned from _prepare_data is wrong' + assert np.ndim(YTY_diag) == 1 and np.ndim(YTDY_diag) == 1 and np.ndim(YTFY_diag) == 1,\ + 'Dimension of YTY_diag etc. returned from _prepare_data is wrong' + assert np.ndim(XTX) == 2 and np.ndim(XTDX) == 2 and np.ndim(XTFX) == 2,\ + 'Dimension of XTX etc. returned from _prepare_data is wrong' + assert np.ndim(X0TX0) == 2 and np.ndim(X0TDX0) == 2 and np.ndim(X0TFX0) == 2,\ + 'Dimension of X0TX0 etc. returned from _prepare_data is wrong' + assert np.ndim(XTX0) == 2 and np.ndim(XTDX0) == 2 and np.ndim(XTFX0) == 2,\ + 'Dimension of XTX0 etc. returned from _prepare_data is wrong' + assert np.ndim(X0TY) == 2 and np.ndim(X0TDY) == 2 and np.ndim(X0TFY) == 2,\ + 'Dimension of X0TY etc. returned from _prepare_data is wrong' l_idx = np.tril_indices(n_C) n_l = np.size(l_idx[0]) + # Make sure all the fields are in the indices. idx_param_sing, idx_param_fitU, idx_param_fitV = brsa._build_index_param(n_l, n_V, 2) - + assert 'Cholesky' in idx_param_sing and 'log_sigma2' in idx_param_sing \ + and 'a1' in idx_param_sing, 'The dictionary for parameter indexing misses some keys' + assert 'Cholesky' in idx_param_fitU and 'a1' in idx_param_fitU, \ + 'The dictionary for parameter indexing misses some keys' + assert 'log_SNR2' in idx_param_fitV and 'c_space' in idx_param_fitV \ + and 'c_inten' in idx_param_fitV and 'c_both' in idx_param_fitV, \ + 'The dictionary for parameter indexing misses some keys' + # Initial parameters are correct parameters with some perturbation param0_fitU = np.random.randn(n_l+n_V) * 0.1 param0_fitV = np.random.randn(n_V+1) * 0.1 - param0_fitV[:n_V-1] += np.log(snr[:n_V-1])*2 - param0_fitV[n_V-1] += np.log(smooth_width)*2 - param0_fitV[n_V] += np.log(inten_kernel)*2 + param0_sing = np.random.randn(n_l+2) * 0.1 + param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 + param0_sing[idx_param_sing['a1']] += np.mean(np.tan(rho1 * np.pi / 2)) + param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 + param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 + param0_fitV[idx_param_fitV['c_inten']] += np.log(inten_kernel)*2 + + # log likelihood and derivative of the _singpara function + ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing) + # We test the gradient to the Cholesky factor + vec = np.zeros(np.size(param0_sing)) + vec[idx_param_sing['Cholesky'][0]] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing)[0], + param0_sing, vec) + assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' + + # We test the gradient to log(sigma^2) + vec = np.zeros(np.size(param0_sing)) + vec[idx_param_sing['log_sigma2']] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing)[0], + param0_sing, vec) + assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' + + # We test the gradient to a1 + vec = np.zeros(np.size(param0_sing)) + vec[idx_param_sing['a1']] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing)[0], + param0_sing, vec) + assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt a1 is incorrect' - # log likelihood and derivative at the initial parameters + + # log likelihood and derivative of the fitU function. ll0, deriv0 = brsa._loglike_AR1_diagV_fitU(param0_fitU, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, \ - XTY, XTDY, XTFY, np.log(snr)*2, l_idx,n_C,n_T,n_V,idx_param_fitU,n_C) + XTY, XTDY, XTFY, np.log(snr)*2, l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C) # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct vec = np.zeros(np.size(param0_fitU)) vec[idx_param_fitU['Cholesky'][0]] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec) + l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], + param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect' # We test the gradient wrt the reparametrization of AR(1) coefficient of noise. @@ -274,7 +345,8 @@ def test_gradient(): vec[idx_param_fitU['a1'][0]] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec) + l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], + param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt to AR(1) coefficient incorrect' # Test on a random direction @@ -282,32 +354,46 @@ def test_gradient(): vec = vec / np.linalg.norm(vec) dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec) + l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], + param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU incorrect' # We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior. + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + brsa._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, + X0TY, X0TDY, X0TFY, L_full, rho1) + assert np.ndim(XTAX) == 3, 'Dimension of XTAX is wrong by _calc_sandwidge()' + assert XTAY.shape == XTY.shape, 'Shape of XTAY is wrong by _calc_sandwidge()' + assert YTAY.shape == YTY_diag.shape, 'Shape of YTAY is wrong by _calc_sandwidge()' + assert np.ndim(X0TAX0) == 3, 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' + assert np.ndim(XTAX0) == 3, 'Dimension of XTAX0 is wrong by _calc_sandwidge()' + assert X0TAY.shape == X0TY.shape, 'Shape of X0TAX0 is wrong by _calc_sandwidge()' ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV[idx_param_fitV['log_SNR2']], - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,idx_param_fitV,n_C,False,False) + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,False,False) vec = np.zeros(np.size(param0_fitV[idx_param_fitV['log_SNR2']])) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, False, False)[0], + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, False, False)[0], param0_fitV[idx_param_fitV['log_SNR2']], vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' # We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,idx_param_fitV,n_C,True,True, + ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,True,True, dist2,inten_diff2,100,100) vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV srt log(SNR2) incorrect for model with GP' @@ -315,9 +401,9 @@ def test_gradient(): # We test the graident wrt spatial length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_space']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt spatial length scale of GP incorrect' @@ -325,9 +411,9 @@ def test_gradient(): # We test the graident wrt intensity length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_inten']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt intensity length scale of GP incorrect' @@ -335,9 +421,9 @@ def test_gradient(): # We test the graident on a random direction vec = np.random.randn(np.size(param0_fitV)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV incorrect' From e0af11e6a09e3f3964d07d2c4f96613823017705 Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 2 Oct 2016 23:16:34 -0400 Subject: [PATCH 05/30] Further changing singpara, preparing to deal with shared time series X0 --- brainiak/reprsimil/brsa.py | 23 ++++++++++++++++------- tests/reprsimil/test_brsa.py | 19 ++++++++++++++----- 2 files changed, 30 insertions(+), 12 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 7d5f5f555..62e385045 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -447,7 +447,7 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, n_run + X0TY, X0TDY, X0TFY, X0, n_run def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): return XTX - rho1 * XTDX + rho1**2 * XTFX @@ -594,7 +594,7 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, n_run \ + X0TY, X0TDY, X0TFY, X0, n_run \ = self._prepare_data(X, Y, n_T, scan_onsets) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and @@ -637,7 +637,9 @@ def _fit_RSA_UV(self, X, Y, current_vec_U_chlsk_l_AR1, current_a1, current_logSigma2 = \ self._initial_fit_singpara( XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X, Y, idx_param_sing, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + X, X0, Y, idx_param_sing, l_idx, n_C, n_T, n_V, n_l, n_run, rank) current_logSNR2 = -current_logSigma2 @@ -771,7 +773,9 @@ def _fit_RSA_UV(self, X, Y, def _initial_fit_singpara(self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X, Y, idx_param_sing, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + X, X0, Y, idx_param_sing, l_idx, n_C, n_T, n_V, n_l, n_run, rank): """ Perform initial fitting of a simplified model, which assumes that all voxels share exactly the same temporal covariance @@ -781,8 +785,9 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, """ logger.info('Initial fitting assuming single parameter of ' 'noise for all voxels') - beta_hat = np.linalg.lstsq(X, Y)[0] - residual = Y - np.dot(X, beta_hat) + X_joint = np.concatenate((X0, X), axis=1) + beta_hat = np.linalg.lstsq(X_joint, Y)[0] + residual = Y - np.dot(X_joint, beta_hat) # point estimates of betas and fitting residuals without assuming # the Bayesian model underlying RSA. @@ -829,7 +834,9 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, res = scipy.optimize.minimize( self._loglike_AR1_singpara, param0, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, options={'disp': self.verbose}) @@ -1404,6 +1411,8 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, l_idx, n_C, n_T, n_V, n_run, idx_param_sing, rank=None): # In this version, we assume that beta is independent diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index a1aea8799..e487db9b0 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -257,7 +257,7 @@ def test_gradient(): # test if the gradients are correct XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, n_run_returned =\ + X0TY, X0TDY, X0TFY, X0, n_run_returned =\ brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ @@ -272,6 +272,7 @@ def test_gradient(): 'Dimension of XTX0 etc. returned from _prepare_data is wrong' assert np.ndim(X0TY) == 2 and np.ndim(X0TDY) == 2 and np.ndim(X0TFY) == 2,\ 'Dimension of X0TY etc. returned from _prepare_data is wrong' + X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) n_l = np.size(l_idx[0]) @@ -297,13 +298,17 @@ def test_gradient(): # log likelihood and derivative of the _singpara function ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing) # We test the gradient to the Cholesky factor vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['Cholesky'][0]] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' @@ -312,7 +317,9 @@ def test_gradient(): vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['log_sigma2']] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' @@ -321,7 +328,9 @@ def test_gradient(): vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['a1']] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt a1 is incorrect' From 4f99ac9cd88d00548239bd850937d00de1dc4f9e Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 6 Oct 2016 14:06:55 -0400 Subject: [PATCH 06/30] Changed the model to consider spatial correlation in noise --- brainiak/reprsimil/brsa.py | 530 ++++++++++-------- ...tational_similarity_estimate_example.ipynb | 271 +++------ tests/reprsimil/test_brsa.py | 173 ++++-- 3 files changed, 476 insertions(+), 498 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 62e385045..39b2559c1 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -92,15 +92,6 @@ class BRSA(BaseEstimator): tol: tolerance parameter passed to the minimizer. verbose : boolean, default: False Verbose mode flag. - pad_DC: boolean, default: False - A column of all 1's will be padded to end of the design matrix - to account for residual baseline component in the signal. - We recommend removing DC component in your data but still - set this as True. If you include a baseline column yourself, - then you should check this as False. - In future version, we will include a seperate input - argument for all regressors you are not interested in, - such as DC component and motion parameters. epsilon: a small number added to the diagonal element of the covariance matrix in the Gaussian Process prior. This is to ensure that the matrix is invertible. @@ -121,7 +112,7 @@ class BRSA(BaseEstimator): tau_range: the reasonable range of the standard deviation of the Gaussian Process. Since the Gaussian Process is imposed on the log(SNR), this range should not be too - large. 5 is a pretty loose range. This parameter is + large. 10 is a pretty loose range. This parameter is used in a half-Cauchy prior on the standard deviation init_iter: how many initial iterations to fit the model without introducing the GP prior before fitting with it, @@ -167,16 +158,15 @@ class BRSA(BaseEstimator): def __init__( self, n_iter=50, rank=None, GP_space=False, GP_inten=False, - tol=2e-3, verbose=False, pad_DC=False, epsilon=0.0001, + tol=2e-3, verbose=False, epsilon=0.0001, space_smooth_range=None, inten_smooth_range=None, - tau_range=5.0, init_iter=20, optimizer='BFGS', rand_seed=0): + tau_range=10.0, init_iter=20, optimizer='BFGS', rand_seed=0): self.n_iter = n_iter self.rank = rank self.GP_space = GP_space self.GP_inten = GP_inten self.tol = tol self.verbose = verbose - self.pad_DC = pad_DC self.epsilon = epsilon # This is a tiny ridge added to the Gaussian Process # covariance matrix template to gaurantee that it is invertible. @@ -207,8 +197,10 @@ def fit(self, X, design, scan_onsets=None, coords=None, the time dimension after proper preprocessing (e.g. spatial alignment), and specify the onsets of each scan in scan_onsets. design: 2-D numpy array, shape=[time_points, conditions] - This is the design matrix. We will automatically pad a column - of all one's if pad_DC is True. + This is the design matrix. It should only include the hypothetic + response for task conditions. You do not need to include + regressors for a DC component or motion parameters, unless with + a strong reason. scan_onsets: optional, an 1-D numpy array, shape=[runs,] this specifies the indices of X which correspond to the onset of each scanning run. For example, if you have two experimental @@ -251,18 +243,13 @@ def fit(self, X, design, scan_onsets=None, coords=None, assert_all_finite(design) assert design.ndim == 2,\ 'The design matrix should be 2 dimension ndarray' - assert (not np.all(np.std(design, axis=0) > 0) and self.pad_DC)\ - or not self.pad_DC, \ - 'You already included DC component in the '\ - 'design matrix. Please set pad_DC as False' + assert np.linalg.matrix_rank(design) == design.shape[1], \ + 'Your design matrix has rank smaller than the number of'\ + ' columns. Some columns can be explained by linear '\ + 'combination of other columns. Please check your design matrix.' assert np.size(design, axis=0) == np.size(X, axis=0),\ 'Design matrix and data do not '\ 'have the same number of time points.' - if self.pad_DC: - logger.info('Padding one more column of 1 to ' - 'the end of design matrix.') - design = np.concatenate((design, - np.ones([design.shape[0], 1])), axis=1) assert self.rank is None or self.rank <= design.shape[1],\ 'Your design matrix has fewer columns than the rank you set' @@ -321,9 +308,6 @@ def fit(self, X, design, scan_onsets=None, coords=None, self._fit_RSA_UV(X=design, Y=X, scan_onsets=scan_onsets, coords=coords, inten=inten) - if self.pad_DC: - self.U_ = self.U_[:-1, :-1] - self.L_ = self.L_[:-1, :self.rank] self.C_ = utils.cov2corr(self.U_) return self @@ -380,6 +364,7 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): F[0, 0] = 0 F[n_T - 1, n_T - 1] = 0 n_run = 1 + run_TRs = np.array([n_T]) else: # Each value in the scan_onsets tells the index at which # a new scan starts. For example, if n_T = 500, and @@ -414,8 +399,8 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): X_base = [] for r_l in run_TRs: - X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)) - res = np.linalg.lstsq(X_base.T, X) + X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)[:, None]) + res = np.linalg.lstsq(X_base, X) if np.any(np.isclose(res[1], 0)): raise ValueError('Your design matrix appears to have ' 'included baseline time series.' @@ -423,11 +408,11 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): ' columns in your design matrix are for ' ' conditions of interest.') if X0 is not None: - res0 = np.linalg.lstsq(X_base.T, X0) + res0 = np.linalg.lstsq(X_base, X0) if not np.any(np.isclose(res0[1], 0)): # No columns in X0 can be explained by the # baseline regressors. So we insert them. - X0 = np.insert(X0, 0, X_base.T, axis=1) + X0 = np.insert(X0, 0, X_base, axis=1) else: logger.warning('Provided regressors for non-interesting ' 'time series already include baseline. ' @@ -435,24 +420,25 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): else: # If a set of regressors for non-interested signals is not # provided, then we simply include one baseline for each run. - X0 = X_base.T + X0 = X_base logger.info('You did not provide time seres of no interest ' 'such as DC component. One trivial regressor of' ' DC component is included for further modeling.' ' The final covariance matrix won''t ' 'reflet them.') + n_base = X0.shape[1] X0TX0, X0TDX0, X0TFX0 = self._make_templates(D, F, X0, X0) XTX0, XTDX0, XTFX0 = self._make_templates(D, F, X, X0) X0TY, X0TDY, X0TFY = self._make_templates(D, F, X0, Y) return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run + X0TY, X0TDY, X0TFY, X0, n_run, n_base def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): return XTX - rho1 * XTDX + rho1**2 * XTFX - def _make_sandwidge_grad(self, XTX, XTDX, XTFX, rho1): + def _make_sandwidge_grad(self, XTDX, XTFX, rho1): return - XTDX + 2 * rho1 * XTFX def _make_templates(self, D, F, X, Y): @@ -463,26 +449,58 @@ def _make_templates(self, D, F, X, Y): def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, L, rho1): + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base): # Calculate the sandwidge terms which put A between X, Y and X0 # These terms are used a lot in the likelihood. But in the _fitV # step, they only need to be calculated once, since A is fixed. # In _fitU step, they need to be calculated at each iteration, # because rho1 changes. XTAY = self._make_sandwidge(XTY, XTDY, XTFY, rho1) - LTXTAY = np.dot(L.T, XTAY) + # dimension: feature*space YTAY = self._make_sandwidge(YTY_diag, YTDY_diag, YTFY_diag, rho1) + # dimension: space, + # A/sigma2 is the inverse of noise covariance matrix in each voxel. + # YTAY means Y'AY XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ * XTDX[np.newaxis, :, :] \ + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] + # dimension: space*feature*feature X0TAX0 = X0TX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ * X0TDX0[np.newaxis, :, :] \ + rho1[:, np.newaxis, np.newaxis]**2 * X0TFX0[np.newaxis, :, :] + # dimension: space*#baseline*#baseline XTAX0 = XTX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ * XTDX0[np.newaxis, :, :] \ + rho1[:, np.newaxis, np.newaxis]**2 * XTFX0[np.newaxis, :, :] + # dimension: space*feature*#baseline X0TAY = self._make_sandwidge(X0TY, X0TDY, X0TFY, rho1) - return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY + # dimension: #baseline*space + X0TAX0_i = np.linalg.solve(X0TAX0, np.identity(n_base)[None, :, :]) + # dimension: space*#baseline*#baseline + XTAcorrX = XTAX.copy() + # dimension: space*feature*feature + XTAcorrY = XTAY.copy() + # dimension: feature*space + for i_v in range(n_V): + XTAcorrX[i_v, :, :] -= \ + np.dot(np.dot(XTAX0[i_v, :, :], X0TAX0_i[i_v, :, :]), + XTAX0[i_v, :, :].T) + XTAcorrY[:, i_v] -= np.dot(np.dot(XTAX0[i_v, :, :], + X0TAX0_i[i_v, :, :]), + X0TAY[:, i_v]) + XTAcorrXL = np.dot(XTAcorrX, L) + # dimension: space*feature*rank + LTXTAcorrXL = np.tensordot(XTAcorrXL, L, axes=(1, 0)) + # dimension: rank*feature*rank + LTXTAcorrY = np.dot(L.T, XTAcorrY) + # dimension: rank*space + YTAcorrY = YTAY - np.sum(X0TAY * np.einsum('ijk,ki->ji', + X0TAX0_i, X0TAY), axis=0) + # dimension: space + + return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL def _calc_dist2_GP(self, coords=None, inten=None, GP_space=False, GP_inten=False): @@ -532,8 +550,7 @@ def _build_index_param(self, n_l, n_V, n_smooth): """ Build dictionaries to retrieve each parameter from the combined parameters. """ - idx_param_sing = {'Cholesky': np.arange(n_l), - 'log_sigma2': n_l, 'a1': n_l + 1} + idx_param_sing = {'Cholesky': np.arange(n_l), 'a1': n_l} # for simplified fitting idx_param_fitU = {'Cholesky': np.arange(n_l), 'a1': np.arange(n_l, n_l + n_V)} @@ -594,7 +611,7 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run \ + X0TY, X0TDY, X0TFY, X0, n_run, n_base \ = self._prepare_data(X, Y, n_T, scan_onsets) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and @@ -640,13 +657,13 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, X, X0, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, n_run, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank) current_logSNR2 = -current_logSigma2 norm_factor = np.mean(current_logSNR2) current_logSNR2 = current_logSNR2 - norm_factor - current_vec_U_chlsk_l_AR1 = current_vec_U_chlsk_l_AR1 \ - * np.exp(norm_factor / 2.0) + # current_vec_U_chlsk_l_AR1 = current_vec_U_chlsk_l_AR1 \ + # * np.exp(norm_factor / 2.0) # Step 2 fitting, which only happens if # GP prior is requested @@ -659,7 +676,7 @@ def _fit_RSA_UV(self, X, Y, current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank) current_GP[0] = np.log(np.min( dist2[np.tril_indices_from(dist2, k=-1)])) @@ -695,7 +712,7 @@ def _fit_RSA_UV(self, X, Y, current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank, + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range) @@ -709,36 +726,24 @@ def _fit_RSA_UV(self, X, Y, est_SNR_AR1_UV = np.exp(current_logSNR2 / 2.0) # Calculating est_sigma_AR1_UV - YTAY = YTY_diag - est_rho1_AR1_UV * YTDY_diag + \ - est_rho1_AR1_UV**2 * YTFY_diag - XTAX = XTX[np.newaxis, :, :] \ - - est_rho1_AR1_UV[:, np.newaxis, np.newaxis] \ - * XTDX[np.newaxis, :, :] \ - + est_rho1_AR1_UV[:, np.newaxis, np.newaxis]**2\ - * XTFX[np.newaxis, :, :] - # dimension: space*feature*feature - XTAY = XTY - est_rho1_AR1_UV * XTDY + est_rho1_AR1_UV**2 * XTFY - # dimension: feature*space - LTXTAY = np.dot(estU_chlsk_l_AR1_UV.T, XTAY) - # dimension: rank*space - - LAMBDA_i = np.zeros([n_V, rank, rank]) - for i_v in range(n_V): - LAMBDA_i[i_v, :, :] = np.dot(np.dot( - estU_chlsk_l_AR1_UV.T, XTAX[i_v, :, :]), estU_chlsk_l_AR1_UV)\ - * est_SNR_AR1_UV[i_v]**2 - LAMBDA_i += np.eye(rank) + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL\ + = self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + estU_chlsk_l_AR1_UV, est_rho1_AR1_UV, + n_V, n_base) + LAMBDA_i = LTXTAcorrXL * est_SNR_AR1_UV[:, None, None]**2 \ + + np.eye(rank) # dimension: space*rank*rank - LAMBDA = np.linalg.inv(LAMBDA_i) + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) # dimension: space*rank*rank - YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) + YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) # dimension: space*rank - YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, estU_chlsk_l_AR1_UV.T) - # dimension: space*feature - - est_sigma_AR1_UV = ((YTAY - est_SNR_AR1_UV**2 * - np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) - / n_T)**0.5 + est_sigma_AR1_UV = ((YTAcorrY - np.sum(LTXTAcorrY + * YTAcorrXL_LAMBDA.T, axis=0) + * est_SNR_AR1_UV**2) / (n_T - n_base)) ** 0.5 t_finish = time.time() logger.info( @@ -775,8 +780,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - X, X0, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, n_run, rank): + X, X0, Y, idx_param_sing, l_idx, + n_C, n_T, n_V, n_l, n_run, n_base, rank): """ Perform initial fitting of a simplified model, which assumes that all voxels share exactly the same temporal covariance matrix for their noise (the same noise variance and @@ -828,7 +833,7 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, # Then we fill each part of the original guess of parameters param0[idx_param_sing['Cholesky']] = current_vec_U_chlsk_l_AR1 param0[idx_param_sing['a1']] = np.median(np.tan(rho1 * np.pi / 2)) - param0[idx_param_sing['log_sigma2']] = np.median(log_sigma2) + # param0[idx_param_sing['log_sigma2']] = np.median(log_sigma2) # Fit it. res = scipy.optimize.minimize( @@ -836,10 +841,10 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, - options={'disp': self.verbose}) + options={'disp': self.verbose, 'maxiter': 100}) current_vec_U_chlsk_l_AR1 = res.x[idx_param_sing['Cholesky']] current_a1 = res.x[idx_param_sing['a1']] * np.ones(n_V) # log(sigma^2) assuming the data include no signal is returned, @@ -856,7 +861,7 @@ def _fit_diagV_noGP( current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank): + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank): """ (optional) second step of fitting, full model but without GP prior on log(SNR). This is only used when GP is requested. @@ -883,19 +888,24 @@ def _fit_diagV_noGP( # fit V, reflected in the log(SNR^2) of each voxel rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, \ + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, - X0TY, X0TDY, X0TFY, L, rho1) + X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=(XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, - LTXTAY, current_vec_U_chlsk_l_AR1, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, + current_vec_U_chlsk_l_AR1, current_a1, l_idx, n_C, n_T, n_V, n_run, - idx_param_fitV, rank, + n_base, idx_param_fitV, rank, False, False), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, @@ -928,8 +938,10 @@ def _fit_diagV_noGP( res_fitU = scipy.optimize.minimize( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, - n_T, n_V, n_run, idx_param_fitU, rank), + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_logSNR2, l_idx, n_C, + n_T, n_V, n_run, n_base, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 3}) @@ -953,8 +965,8 @@ def _fit_diagV_GP( XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, - idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank, GP_space, GP_inten, + idx_param_fitU, idx_param_fitV, l_idx, + n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range): """ Last step of fitting. If GP is not requested, it will still fit. @@ -988,18 +1000,24 @@ def _fit_diagV_GP( # fit V rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, \ + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, - X0TY, X0TDY, X0TFY, L, rho1) + X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=( - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, + XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, current_vec_U_chlsk_l_AR1, current_a1, - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, rank, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range), method=self.optimizer, jac=True, @@ -1030,8 +1048,10 @@ def _fit_diagV_GP( res_fitU = scipy.optimize.minimize( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, n_T, n_V, - n_run, idx_param_fitU, rank), + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_logSNR2, l_idx, n_C, n_T, n_V, + n_run, n_base, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, @@ -1067,7 +1087,9 @@ def _fit_diagV_GP( def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - log_SNR2, l_idx, n_C, n_T, n_V, n_run, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + log_SNR2, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitU, rank): # This function calculates the log likelihood of data given cholesky # decomposition of U and AR(1) parameters of noise as free parameters. @@ -1099,10 +1121,6 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # Such parametrization avoids the need of boundaries # for parameters. - # n_l = np.size(l_idx[0]) - # the number of parameters in the index of lower-triangular matrix - # This indexing allows for parametrizing only - # part of the lower triangular matrix (non-full rank covariance matrix) L = np.zeros([n_C, rank]) # lower triagular matrix L, cholesky decomposition of U L[l_idx] = param[idx_param_fitU['Cholesky']] @@ -1114,79 +1132,114 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # each element of SNR2 is the ratio of the diagonal element on V # to the variance of the fresh noise in that voxel - YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag - # dimension: space, - # A/sigma2 is the inverse of noise covariance matrix in each voxel. - # YTAY means Y'AY - XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis]\ - * XTDX[np.newaxis, :, :] + rho1[:, np.newaxis, np.newaxis]**2\ - * XTFX[np.newaxis, :, :] - # dimension: space*feature*feature - XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY - # dimension: feature*space - LTXTAY = np.dot(L.T, XTAY) - # dimension: rank*space - # LAMBDA_i = np.zeros([n_V, rank, rank]) - # for i_v in range(n_V): - # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L)\ - # * SNR2[i_v] - # LAMBDA_i += np.eye(rank) - # LTXTAXL = np.empty([n_V, rank, rank]) - # for i_v in range(n_V): - # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) - LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) - LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, \ + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ + self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base) + + # Only starting from this point, SNR2 is involved + LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank - LAMBDA = np.linalg.inv(LAMBDA_i) + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) # dimension: space*rank*rank # LAMBDA is essentially the inverse covariance matrix of the # posterior probability of alpha, which bears the relation with # beta by beta = L * alpha, and L is the Cholesky factor of the # shared covariance matrix U. refer to the explanation below # Equation 5 in the NIPS paper. - YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) - # dimension: space*rank - YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) - # dimension: space*feature (feature can be larger than rank) - # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) \ - # / n_T - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ - / n_T - # dimension: space, + # LAMBDA_LTXTAcorrY = np.einsum('ijk,ki->ji', LAMBDA_i, LTXTAcorrY) + YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) + # dimension: space*rank + # # dimension: feature*space + sigma2 = (YTAcorrY - np.sum(LTXTAcorrY * YTAcorrXL_LAMBDA.T, axis=0) + * SNR2) / (n_T - n_base) - LL = -np.sum(np.log(sigma2)) * n_T * 0.5 \ + LL = - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5 \ + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ + - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5 \ - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ - - n_T / 2.0 - # log likelihood - XTAXL = np.dot(XTAX, L) - # dimension: space*feature*rank - deriv_L = -np.einsum('ijk,ikl,i', XTAXL, LAMBDA, SNR2) \ - - np.dot(np.einsum('ijk,ik->ji', XTAXL, YTAXL_LAMBDA) * SNR2**2 - / sigma2, YTAXL_LAMBDA) \ - + np.dot(XTAY / sigma2 * SNR2, YTAXL_LAMBDA) - # - np.einsum('ijk,ik,il,i', XTAXL, YTAXL_LAMBDA, YTAXL_LAMBDA, - # SNR2**2 / sigma2) \ + - (n_T - n_base) * n_V * (1 + np.log(2 * np.pi)) * 0.5 + if not np.isfinite(LL): + print('NaN detected!') + print(sigma2) + print(YTAcorrY) + print(LTXTAcorrY) + print(YTAcorrXL_LAMBDA) + print(SNR2) + + YTAcorrXL_LAMBDA_LT = np.dot(YTAcorrXL_LAMBDA, L.T) + # dimension: space*feature (feature can be larger than rank) + deriv_L = -np.einsum('ijk,ikl,i', XTAcorrXL, LAMBDA, SNR2) \ + - np.dot(np.einsum('ijk,ik->ji', XTAcorrXL, YTAcorrXL_LAMBDA) + * SNR2**2 / sigma2, YTAcorrXL_LAMBDA) \ + + np.dot(XTAcorrY / sigma2 * SNR2, YTAcorrXL_LAMBDA) # dimension: feature*rank + + # The following are for calculating the derivative to a1 + deriv_a1 = np.empty(n_V) dXTAX_drho1 = -XTDX + 2 * rho1[:, np.newaxis, np.newaxis] * XTFX # dimension: space*feature*feature - dXTAY_drho1 = -XTDY + 2 * rho1 * XTFY + dXTAY_drho1 = self._make_sandwidge_grad(XTDY, XTFY, rho1) # dimension: feature*space - dYTAY_drho1 = -YTDY_diag + 2 * rho1 * YTFY_diag - # dimension: space, - deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) * \ - (-n_run * rho1 / (1 - rho1**2) - - np.einsum('...ij,...ji', np.dot(LAMBDA, L.T), - np.dot(dXTAX_drho1, L)) * SNR2 / 2.0 - + np.sum(dXTAY_drho1 * YTAXL_LAMBDA_LT.T, axis=0) - / sigma2 * SNR2 - - np.einsum('...i,...ij,...j', - YTAXL_LAMBDA_LT, dXTAX_drho1, YTAXL_LAMBDA_LT) - / sigma2 / 2.0 * (SNR2**2.0) - - dYTAY_drho1 / (sigma2 * 2.0)) + dYTAY_drho1 = self._make_sandwidge_grad(YTDY_diag, YTFY_diag, rho1) # dimension: space, + dX0TAX0_drho1 = - X0TDX0 \ + + 2 * rho1[:, np.newaxis, np.newaxis] * X0TFX0 + # dimension: space*rank*rank + dXTAX0_drho1 = - XTDX0 \ + + 2 * rho1[:, np.newaxis, np.newaxis] * XTFX0 + # dimension: space*feature*rank + dX0TAY_drho1 = self._make_sandwidge_grad(X0TDY, X0TFY, rho1) + # dimension: rank*space + + # The following are executed for each voxel. + for i_v in range(n_V): + # All variables with _ele as suffix are for data of just one voxel + invX0TAX0_X0TAX_ele = np.dot(X0TAX0_i[i_v, :, :], + XTAX0[i_v, :, :].T) + invX0TAX0_X0TAY_ele = np.dot(X0TAX0_i[i_v, :, :], X0TAY[:, i_v]) + dXTAX0_drho1_invX0TAX0_X0TAX_ele = np.dot(dXTAX0_drho1[i_v, :, :], + invX0TAX0_X0TAX_ele) + # preparation for the variable below + dXTAcorrX_drho1_ele = dXTAX_drho1[i_v, :, :] \ + - dXTAX0_drho1_invX0TAX0_X0TAX_ele \ + - dXTAX0_drho1_invX0TAX0_X0TAX_ele.T \ + + np.dot(np.dot(invX0TAX0_X0TAX_ele.T, + dX0TAX0_drho1[i_v, :, :]), + invX0TAX0_X0TAX_ele) + dXTAcorrY_drho1_ele = dXTAY_drho1[:, i_v] \ + - np.dot(invX0TAX0_X0TAX_ele.T, dX0TAY_drho1[:, i_v]) \ + - np.dot(dXTAX0_drho1[i_v, :, :], invX0TAX0_X0TAY_ele) \ + + np.dot(np.dot(invX0TAX0_X0TAX_ele.T, + dX0TAX0_drho1[i_v, :, :]), + invX0TAX0_X0TAY_ele) + dYTAcorrY_drho1_ele = dYTAY_drho1[i_v] \ + - np.dot(dX0TAY_drho1[:, i_v], invX0TAX0_X0TAY_ele) * 2\ + + np.dot(np.dot(invX0TAX0_X0TAY_ele, dX0TAX0_drho1[i_v, :, :]), + invX0TAX0_X0TAY_ele) + deriv_a1[i_v] = 2 / np.pi / (1 + a1[i_v]**2) \ + * (- n_run * rho1[i_v] / (1 - rho1[i_v]**2) + - np.einsum('ij,ij', X0TAX0_i[i_v, :, :], + dX0TAX0_drho1[i_v, :, :]) * 0.5 + - np.einsum('ij,ij', LAMBDA[i_v, :, :], + np.dot(np.dot( + L.T, dXTAcorrX_drho1_ele), L)) + * (SNR2[i_v] * 0.5) + - dYTAcorrY_drho1_ele * 0.5 / sigma2[i_v] + + SNR2[i_v] / sigma2[i_v] + * np.dot(dXTAcorrY_drho1_ele, + YTAcorrXL_LAMBDA_LT[i_v, :]) + - (0.5 * SNR2[i_v]**2 / sigma2[i_v]) + * np.dot(np.dot(YTAcorrXL_LAMBDA_LT[i_v, :], + dXTAcorrX_drho1_ele), + YTAcorrXL_LAMBDA_LT[i_v, :])) + deriv = np.zeros(np.size(param)) deriv[idx_param_fitU['Cholesky']] = deriv_L[l_idx] deriv[idx_param_fitU['a1']] = deriv_a1 @@ -1194,9 +1247,11 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, return -LL, -deriv def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, - X0TAX0, XTAX0, X0TAY, LTXTAY, + X0TAX0, XTAX0, X0TAY, X0TAX0_i, + XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_l, a1, l_idx, n_C, n_T, n_V, n_run, - idx_param_fitV, rank=None, + n_base, idx_param_fitV, rank=None, GP_space=False, GP_inten=False, dist2=None, inten_dist2=None, space_smooth_range=None, @@ -1248,53 +1303,34 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # If requested, a GP prior is imposed on log(SNR). rho1 = 2.0 / np.pi * np.arctan(a1) # AR(1) coefficient, dimension: space - # YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag - # dimension: space, - # XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ - # * XTDX[np.newaxis, :, :] \ - # + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] - # dimension: space*feature*feature - # XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY - # dimension: feature*space - LTXTAY = np.dot(L.T, XTAY) - # dimension: rank*space - # LAMBDA_i = np.zeros([n_V, rank, rank]) - # for i_v in range(n_V): - # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) \ - # * SNR2[i_v] - # LAMBDA_i += np.eye(rank) - # LTXTAXL = np.empty([n_V, rank, rank]) - # for i_v in range(n_V): - # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) - LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) - LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) + LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank - LAMBDA = np.linalg.inv(LAMBDA_i) + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) # dimension: space*rank*rank - YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) + YTAcorrXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAcorrY) # dimension: space*rank - # YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) - # dimension: space*feature - # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1))\ - # / n_T - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ - / n_T + sigma2 = (YTAcorrY + - SNR2 * np.sum(YTAcorrXL_LAMBDA + * LTXTAcorrY.T, axis=1)) / (n_T - n_base) # dimension: space - LL = -np.sum(np.log(sigma2)) * n_T * 0.5\ + LL = - (n_T - n_base) * np.log(2 * np.pi) * 0.5\ + - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5\ + np.sum(np.log(1 - rho1**2)) * n_run * 0.5\ - - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 - n_T * 0.5 + - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5\ + - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5\ + - (n_T - n_base) * n_V * 0.5 # Log likelihood of data given parameters, without the GP prior. deriv_log_SNR2 = (-rank + np.trace(LAMBDA, axis1=1, axis2=2)) * 0.5\ - + YTAY / (sigma2 * 2.0) - n_T * 0.5 \ - - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA, - LTXTAXL, YTAXL_LAMBDA)\ + + YTAcorrY / (sigma2 * 2.0) - (n_T - n_base) * 0.5 \ + - np.einsum('ij,ijk,ik->i', YTAcorrXL_LAMBDA, + LTXTAcorrXL, YTAcorrXL_LAMBDA)\ / (sigma2 * 2.0) * (SNR2**2) - # - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA_LT, - # XTAX, YTAXL_LAMBDA_LT)\ # Partial derivative of log likelihood over log(SNR^2) # dimension: space, + # The second term above is due to the equation for calculating + # sigma2 if GP_space: # Imposing GP prior on log(SNR) at least over # spatial coordinates @@ -1413,7 +1449,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing, rank=None): # In this version, we assume that beta is independent # between voxels and noise is also independent. @@ -1432,62 +1468,84 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, L = np.zeros([n_C, rank]) L[l_idx] = param[idx_param_sing['Cholesky']] - log_sigma2 = param[idx_param_sing['log_sigma2']] - sigma2 = np.exp(log_sigma2) a1 = param[idx_param_sing['a1']] rho1 = 2.0 / np.pi * np.arctan(a1) XTAX = XTX - rho1 * XTDX + rho1**2 * XTFX - LAMBDA_i = np.eye(rank) +\ - np.dot(np.dot(L.T, XTAX), L) / sigma2 + X0TAX0 = X0TX0 - rho1 * X0TDX0 + rho1**2 * X0TFX0 + XTAX0 = XTX0 - rho1 * XTDX0 + rho1**2 * XTFX0 + XTAcorrX = XTAX - np.dot(XTAX0, np.linalg.solve(X0TAX0, XTAX0.T)) + XTAcorrXL = np.dot(XTAcorrX, L) + LAMBDA_i = np.dot(np.dot(L.T, XTAcorrX), L) + np.eye(rank) XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY - LTXTAY = np.dot(L.T, XTAY) + X0TAY = X0TY - rho1 * X0TDY + rho1**2 * X0TFY + XTAcorrY = XTAY - np.dot(XTAX0, np.linalg.solve(X0TAX0, X0TAY)) + LTXTAcorrY = np.dot(L.T, XTAcorrY) YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag - - LAMBDA_LTXTAY = np.linalg.solve(LAMBDA_i, LTXTAY) - L_LAMBDA_LTXTAY = np.dot(L, LAMBDA_LTXTAY) - - LL = np.sum(LTXTAY * LAMBDA_LTXTAY) / (sigma2**2 * 2.0) \ - - np.sum(YTAY) / (sigma2 * 2.0) - - deriv_L = np.dot(XTAY, LAMBDA_LTXTAY.T) / sigma2**2 \ - - np.dot(np.dot(XTAX, L_LAMBDA_LTXTAY), - LAMBDA_LTXTAY.T) / sigma2**3 - - deriv_log_sigma2 = np.sum(YTAY) / (sigma2 * 2.0) \ - - np.sum(XTAY * L_LAMBDA_LTXTAY) / (sigma2**2) \ - + np.sum(np.dot(XTAX, L_LAMBDA_LTXTAY) - * L_LAMBDA_LTXTAY) / (sigma2**3 * 2.0) + YTAcorrY = YTAY \ + - np.sum(X0TAY * np.linalg.solve(X0TAX0, X0TAY), axis=0) + + LAMBDA_LTXTAcorrY = np.linalg.solve(LAMBDA_i, LTXTAcorrY) + L_LAMBDA_LTXTAcorrY = np.dot(L, LAMBDA_LTXTAcorrY) + + sigma2 = np.mean(YTAcorrY - + np.sum(LTXTAcorrY * LAMBDA_LTXTAcorrY, axis=0))\ + / (n_T - n_base) + LL = n_V * (-np.log(sigma2) * (n_T - n_base) * 0.5 + + np.log(1 - rho1**2) * n_run * 0.5 + - np.log(np.linalg.det(X0TAX0)) * 0.5 + - np.log(np.linalg.det(LAMBDA_i)) * 0.5) + + deriv_L = np.dot(XTAcorrY, LAMBDA_LTXTAcorrY.T) / sigma2 \ + - np.dot(np.dot(XTAcorrXL, LAMBDA_LTXTAcorrY), + LAMBDA_LTXTAcorrY.T) / sigma2 \ + - np.linalg.solve(LAMBDA_i, XTAcorrXL.T).T * n_V + + # These terms are used to construct derivative to a1. + dXTAX_drho1 = - XTDX + 2 * rho1 * XTFX + dX0TAX0_drho1 = - X0TDX0 + 2 * rho1 * X0TFX0 + dXTAX0_drho1 = - XTDX0 + 2 * rho1 * XTFX0 + invX0TAX0_X0TAX = np.linalg.solve(X0TAX0, XTAX0.T) + dXTAX0_drho1_invX0TAX0_X0TAX = np.dot(dXTAX0_drho1, invX0TAX0_X0TAX) + + dXTAcorrX_drho1 = dXTAX_drho1 - dXTAX0_drho1_invX0TAX0_X0TAX \ + - dXTAX0_drho1_invX0TAX0_X0TAX.T \ + + np.dot(np.dot(invX0TAX0_X0TAX.T, dX0TAX0_drho1), + invX0TAX0_X0TAX) + dLTXTAcorrXL_drho1 = np.dot(np.dot(L.T, dXTAcorrX_drho1), L) + + dYTAY_drho1 = - YTDY_diag + 2 * rho1 * YTFY_diag + dX0TAY_drho1 = - X0TDY + 2 * rho1 * X0TFY + invX0TAX0_X0TAY = np.linalg.solve(X0TAX0, X0TAY) + dYTAX0_drho1_invX0TAX0_X0TAY = np.sum(dX0TAY_drho1 + * invX0TAX0_X0TAY, axis=0) + + dYTAcorrY_drho1 = dYTAY_drho1 - dYTAX0_drho1_invX0TAX0_X0TAY * 2\ + + np.sum(invX0TAX0_X0TAY * + np.dot(dX0TAX0_drho1, invX0TAX0_X0TAY), axis=0) + + dXTAY_drho1 = - XTDY + 2 * rho1 * XTFY + dXTAcorrY_drho1 = dXTAY_drho1 \ + - np.dot(dXTAX0_drho1, invX0TAX0_X0TAY) \ + - np.dot(invX0TAX0_X0TAX.T, dX0TAY_drho1) \ + + np.dot(np.dot(invX0TAX0_X0TAX.T, dX0TAX0_drho1), + invX0TAX0_X0TAY) deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) \ - * (-n_run * rho1 / (1 - rho1**2) - + np.sum((-XTDY + 2 * rho1 * XTFY) - * L_LAMBDA_LTXTAY) / (sigma2**2) - - np.sum(np.dot((-XTDX + 2 * rho1 * XTFX), L_LAMBDA_LTXTAY) - * L_LAMBDA_LTXTAY) / (sigma2**3 * 2.0) - - np.sum(-YTDY_diag + 2 * rho1 * YTFY_diag) / (sigma2 * 2.0)) - - LL = LL + np.size(YTY_diag) * (-log_sigma2 * n_T * 0.5 - + np.log(1 - rho1**2) * n_run * 0.5 - - np.log(np.linalg.det(LAMBDA_i)) - * 0.5) - - deriv_L = deriv_L - np.linalg.solve(LAMBDA_i, np.dot(L.T, XTAX)).T\ - / sigma2 * np.size(YTY_diag) - deriv_log_sigma2 = deriv_log_sigma2 \ - + (rank - n_T - np.trace(np.linalg.inv(LAMBDA_i)))\ - * 0.5 * np.size(YTY_diag) - deriv_a1 = deriv_a1 - np.trace( - np.linalg.solve(LAMBDA_i, - np.dot(np.dot(L.T, - (-XTDX + 2 * rho1 * XTFX)), L)))\ - / (sigma2 * 2) * np.size(YTY_diag) + * (n_V * (- n_run * rho1 / (1 - rho1**2) + - 0.5 * np.trace(np.linalg.solve( + X0TAX0, dX0TAX0_drho1)) + - 0.5 * np.trace(np.linalg.solve( + LAMBDA_i, dLTXTAcorrXL_drho1))) + - 0.5 * np.sum(dYTAcorrY_drho1) / sigma2 + + np.sum(dXTAcorrY_drho1 * L_LAMBDA_LTXTAcorrY) / sigma2 + - 0.5 * np.sum(np.dot(dXTAcorrX_drho1, L_LAMBDA_LTXTAcorrY) + * L_LAMBDA_LTXTAcorrY) / sigma2) deriv = np.zeros(np.size(param)) - deriv[0:n_l] = deriv_L[l_idx] - deriv[n_l] = deriv_log_sigma2 - deriv[n_l + 1] = deriv_a1 + deriv[idx_param_sing['Cholesky']] = deriv_L[l_idx] + deriv[idx_param_sing['a1']] = deriv_a1 return -LL, -deriv diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index aa96a5f06..187727706 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -1,8 +1,12 @@ { "cells": [ { - "cell_type": "markdown", - "metadata": {}, + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], "source": [ "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset." ] @@ -16,7 +20,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "collapsed": false }, @@ -32,7 +36,7 @@ "import numdifftools as nd\n", "import matplotlib.pyplot as plt\n", "import logging\n", - "np.random.seed(100)" + "np.random.seed(10)" ] }, { @@ -44,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": { "collapsed": false }, @@ -80,22 +84,11 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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9vXHs2DGEhIT87Xnp4+HhAa1Wi7Nnz6ruSN26dQuZmZlP1eaOHz+Os2fPYvHi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\nSUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "design = utils.ReadDesign(fname=\"example_design.1D\")\n", "\n", @@ -107,7 +100,7 @@ "fig = plt.figure(num=None, figsize=(12, 3), dpi=150, facecolor='w', edgecolor='k')\n", "\n", "plt.plot(design.design_used)\n", - "plt.ylim([-0.2,1.2])\n", + "plt.ylim([-0.2,0.4])\n", "plt.title('hypothetic fMRI response time courses of all conditions in addition to a DC component\\n'\n", " '(design matrix)')\n", "plt.xlabel('time')\n", @@ -133,22 +126,11 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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PwohPZnR0mKvhqSLdPDD5uT6eNHd2uk+gE91x8zNge3lmJpCeHvsAt3Ah8N57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\nLFvMVdIddvZydQ9YwLSY+1G67bKXq0p3Xp7Vos6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p5u/q9vKwlG4n0q3vHKRCn0+rSndb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\n9ttv47DDDnP9bWHhPAwatBjAYsyfvxiLFy/GrFmzLErQpk00ELByaGf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I6C4tSlJ0n3km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\nt0ac7vIjFtG9ePFiL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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "noise_bot = 0.5\n", "noise_top = 1.5\n", @@ -169,6 +151,7 @@ "for i_t in range(1,n_T):\n", " noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", "# Here, we assume noise is independent between voxels\n", + "noise = noise + np.random.randn(n_V)\n", "fig = plt.figure(num=None, figsize=(12, 2), dpi=150, facecolor='w', edgecolor='k')\n", "plt.plot(noise[:,0])\n", "plt.title('noise in an example voxel')\n", @@ -199,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": { "collapsed": false }, @@ -224,39 +207,17 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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AiaSud99Hb2bWjwJXGTuPNKV1IRunjI0GZgJIOgsYHxFHZY8/ASwlxbZtSGO6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\nSqzzQuDKiPh5iXUeAvxe0ux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axHxYOOiOUENZ09br4VrZPL1gZlYiZy+YmVlbPNI1s8oraj3d4eCga2aVV+R6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\nPR07VKOA6yPi1OzxjZJeRVp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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# ideal covariance matrix\n", "ideal_cov = np.zeros([n_C,n_C])\n", "ideal_cov = np.eye(n_C)*0.6\n", - "ideal_cov[0,0] = 0.1\n", - "ideal_cov[9:13,9:13] = 0.8\n", - "for cond in range(9,13):\n", + "ideal_cov[8:12,8:12] = 0.8\n", + "for cond in range(8,12):\n", " ideal_cov[cond,cond] = 1\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", @@ -291,49 +252,18 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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AEBAQAJ7nMX78eHTs2FHnYKcsOTg4AACePn2KmjVrit57+vSp1oH1ClNPl2Zn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FvONxWB0IxUOGd33Pp9vTrYxn4/mAEH0Qc9QzcgYjU1mjQzehHjWHUdmKUKjPou7aXMhRD8aC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\n9u3bTVZW1pT3k5KSzM6dO/2fDw4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gQQYAV18NfOc7wK5d3rZH8Ad791JlcqNVy0RUivYj0YS+64V6Vxf9/7Zt9NjI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\n0TvqeXn2awyJUBe0iFCPE23oe0kJXYx6V0+b6+y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kCGnDkSIJ9WRy1K2E+u7dobm6ZkJd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AewfAv1QYPIJcxVqLuVZ+vtpZDMQnDUUyngy18G/u3fjMRydvvUc80SW1MTXjK5fDjqhw8HdzYu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\nQm9vr+v/3nnnnRg1ahRqampw4YUXoqWlJ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4G4AtR/JaZjZxDIxeaOeoa0t3pD8K1qB0OTQP4HuyeszMbELzkDEzqz3PSBva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\n13AkbS3pQkmPVvXdZZCYI6u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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "\n", "\n", "L_full = np.linalg.cholesky(ideal_cov) \n", "\n", "# generating signal\n", - "snr_level = 0.5\n", + "snr_level = 0.6\n", "# Notice that accurately speaking this is not snr. the magnitude of signal depends\n", "# not only on beta but also on x. (noise_level*snr_level)**2 is the factor multiplied\n", "# with ideal_cov to form the covariance matrix from which the response amplitudes (beta)\n", @@ -377,7 +307,7 @@ "signal = np.dot(design.design_used,betas_simulated)\n", "\n", "\n", - "Y = signal + noise\n", + "Y = signal + noise \n", "# The data to be fed to the program.\n", "\n", "\n", @@ -422,19 +352,11 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "scan onsets: [ 0. 186.]\n" - ] - } - ], + "outputs": [], "source": [ "scan_onsets = np.linspace(0,design.n_TR,num=n_run+1)[:-1]\n", "print('scan onsets: {}'.format(scan_onsets))" @@ -449,25 +371,11 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "BRSA(GP_inten=True, GP_space=True, epsilon=0.0001, init_iter=20,\n", - " inten_smooth_range=None, n_iter=50, optimizer='BFGS', pad_DC=False,\n", - " rand_seed=0, rank=None, space_smooth_range=None, tau_range=10,\n", - " tol=0.002, verbose=False)" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "brsa = BRSA(GP_space=True,GP_inten=True,tau_range=10)\n", "# Initiate an instance, telling it that we want to impose Gaussian Process prior over both space and intensity.\n", @@ -487,32 +395,11 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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XqH9yzFcIoTE/E+t9lDBbPddCxpgCF7M4L2I13GVmDybG/wJwDbBt4jF/Z0KM6Y7UmP5K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\ntjE0deYcc3HtS0j94jiOUx9taHNu2sx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7AFsDT7dWNeecc41oumulkcnYJb0bOA3YHbgyTwWdc877yLO1vY88BvdzgVPM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\nAprggdw5V3qV2+6bzVOPmV0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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(brsa.C_, vmin=-0.1, vmax=1)\n", @@ -546,36 +433,16 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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tVKXJAcA44D3x7/uAl1k0iWZ/3F/a3p/mMEs0Esd8ExkMem2/suM4Tgpa52Oe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\nKT5idhyn8PjMP8dxnILRaTP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dC/tpnZ+tlf2sYllSQ3RtYBFwE7BDRHS9wdnH03yY2cDoUVdGRPyhUcqI2Lfm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\nubCLgNfX7DuVtFTLMfWDspm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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "betas_point = np.linalg.lstsq(design.design_used, Y)[0]\n", - "point_corr = np.corrcoef(betas_point)\n", - "point_cov = np.cov(betas_point) \n", + "regressor = np.insert(design.design_used,0,1,axis=1)\n", + "betas_point = np.linalg.lstsq(regressor, Y)[0]\n", + "point_corr = np.corrcoef(betas_point[1:,:])\n", + "point_cov = np.cov(betas_point[1:,:])\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(point_corr, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", @@ -608,32 +475,11 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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1u9T+4xh+vfNtrL1+9XCG/45p2AaySNpf0s8lPSlpQNK7ql7/frG98nF1bjtm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\nMDEz/tLMb8MvKvGR8Td54Rv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Z8TXq4AUMLZOMzMysHx38nVGL5kgzMxtOPDIyM2sXHTwycjIyM2sXXk1nZmY2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\n4y/7zUIXdu7XZw+7Km+Hbc/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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "fig = plt.figure(num=None, figsize=(5, 5), dpi=100)\n", "plt.pcolor(np.reshape(brsa.nSNR_, [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", @@ -654,23 +500,11 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "RMS error of Bayesian RSA: 0.13665981702261623\n", - "RMS error of standard RSA: 0.1433569522028947\n", - "Recovered spatial smoothness length scale: 5.595133988654466, vs. true value: 3.0\n", - "Recovered intensity smoothness length scale: 4.611783121422689, vs. true value: 4.0\n", - "Recovered standard deviation of GP prior: 0.184521447350508, vs. true value: 0.8\n" - ] - } - ], + "outputs": [], "source": [ "RMS_BRSA = np.mean((brsa.C_ - ideal_corr)**2)**0.5\n", "RMS_RSA = np.mean((point_corr - ideal_corr)**2)**0.5\n", @@ -687,6 +521,31 @@ "source": [ "#### Empirically, the smoothness turns to be over-estimated when signal is weak." ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.scatter(brsa.sigma_, noise_level)\n", + "plt.show()\n", + "plt.scatter(brsa.rho_, rho1)\n", + "plt.show()\n", + "plt.scatter(brsa.nSNR_, snr)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index e487db9b0..903a9b3a3 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -27,7 +27,7 @@ def test_can_instantiate(): features = 3 s = brainiak.reprsimil.brsa.BRSA(n_iter=50, rank=5, GP_space=True, GP_inten=True, tol=2e-3,\ - pad_DC=False,epsilon=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) + epsilon=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) assert s, "Invalid BRSA instance!" def test_fit(): @@ -70,7 +70,6 @@ def test_fit(): # ideal covariance matrix ideal_cov = np.zeros([n_C,n_C]) ideal_cov = np.eye(n_C)*0.6 - ideal_cov[0,0] = 0.2 ideal_cov[5:9,5:9] = 0.6 for cond in range(5,9): ideal_cov[cond,cond] = 1 @@ -133,7 +132,28 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" - + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + + # Test fitting with lower rank + rank = n_C - 1 + brsa = BRSA(rank=rank) + brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, + coords=coords, inten=inten) + u_b = brsa.U_[1:,1:] + u_i = ideal_cov[1:,1:] + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" + # check that the recovered SNRs makes sense + p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] + assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" # Test fitting without GP prior. brsa = BRSA() @@ -148,6 +168,10 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" assert not hasattr(brsa,'bGP_') and not hasattr(brsa,'lGPspace_') and not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of GP if GP is not requested.' # GP parameters are not set if not requested @@ -164,6 +188,10 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" assert not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of lGPinten_ if only smoothness in space is requested.' # GP parameters are not set if not requested @@ -252,12 +280,12 @@ def test_gradient(): # Test fitting with GP prior. - brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) + brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,rank=n_C) # test if the gradients are correct XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run_returned =\ + X0TY, X0TDY, X0TFY, X0, n_run_returned, n_base =\ brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ @@ -274,12 +302,15 @@ def test_gradient(): 'Dimension of X0TY etc. returned from _prepare_data is wrong' X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) + # rank = n_C - 1 + # idx_rank = np.where(l_idx[1] < rank) + # l_idx = (l_idx[0][idx_rank], l_idx[1][idx_rank]) n_l = np.size(l_idx[0]) # Make sure all the fields are in the indices. idx_param_sing, idx_param_fitU, idx_param_fitV = brsa._build_index_param(n_l, n_V, 2) - assert 'Cholesky' in idx_param_sing and 'log_sigma2' in idx_param_sing \ - and 'a1' in idx_param_sing, 'The dictionary for parameter indexing misses some keys' + assert 'Cholesky' in idx_param_sing and 'a1' in idx_param_sing, \ + 'The dictionary for parameter indexing misses some keys' assert 'Cholesky' in idx_param_fitU and 'a1' in idx_param_fitU, \ 'The dictionary for parameter indexing misses some keys' assert 'log_SNR2' in idx_param_fitV and 'c_space' in idx_param_fitV \ @@ -289,8 +320,8 @@ def test_gradient(): # Initial parameters are correct parameters with some perturbation param0_fitU = np.random.randn(n_l+n_V) * 0.1 param0_fitV = np.random.randn(n_V+1) * 0.1 - param0_sing = np.random.randn(n_l+2) * 0.1 - param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 + param0_sing = np.random.randn(n_l+1) * 0.1 + # param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 param0_sing[idx_param_sing['a1']] += np.mean(np.tan(rho1 * np.pi / 2)) param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 @@ -300,7 +331,7 @@ def test_gradient(): ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing) # We test the gradient to the Cholesky factor vec = np.zeros(np.size(param0_sing)) @@ -308,21 +339,21 @@ def test_gradient(): dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' # We test the gradient to log(sigma^2) - vec = np.zeros(np.size(param0_sing)) - vec[idx_param_sing['log_sigma2']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, - idx_param_sing)[0], - param0_sing, vec) - assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' + # vec = np.zeros(np.size(param0_sing)) + # vec[idx_param_sing['log_sigma2']] = 1 + # dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + # XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + # XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + # l_idx, n_C, n_T, n_V, n_run, n_base, + # idx_param_sing)[0], + # param0_sing, vec) + # assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' # We test the gradient to a1 vec = np.zeros(np.size(param0_sing)) @@ -330,79 +361,100 @@ def test_gradient(): dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt a1 is incorrect' # log likelihood and derivative of the fitU function. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitU(param0_fitU, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, \ - XTY, XTDY, XTFY, np.log(snr)*2, l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C) - - # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct - vec = np.zeros(np.size(param0_fitU)) - vec[idx_param_fitU['Cholesky'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ - YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], - param0_fitU, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect' + ll0, deriv0 = brsa._loglike_AR1_diagV_fitU(param0_fitU, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx,n_C,n_T,n_V,n_run,n_base,idx_param_fitU,n_C) + # We test the gradient wrt the reparametrization of AR(1) coefficient of noise. vec = np.zeros(np.size(param0_fitU)) vec[idx_param_fitU['a1'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ - YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], - param0_fitU, vec) + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitU, n_C)[0], param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt to AR(1) coefficient incorrect' + # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct + vec = np.zeros(np.size(param0_fitU)) + vec[idx_param_fitU['Cholesky'][0]] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run,n_base, + idx_param_fitU, n_C)[0], param0_fitU, vec) + assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect' + # Test on a random direction vec = np.random.randn(np.size(param0_fitU)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ - YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], - param0_fitU, vec) + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitU, n_C)[0], param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU incorrect' # We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior. - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ brsa._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, - X0TY, X0TDY, X0TFY, L_full, rho1) + X0TY, X0TDY, X0TFY, + L_full, rho1, n_V, n_base) assert np.ndim(XTAX) == 3, 'Dimension of XTAX is wrong by _calc_sandwidge()' assert XTAY.shape == XTY.shape, 'Shape of XTAY is wrong by _calc_sandwidge()' assert YTAY.shape == YTY_diag.shape, 'Shape of YTAY is wrong by _calc_sandwidge()' assert np.ndim(X0TAX0) == 3, 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' assert np.ndim(XTAX0) == 3, 'Dimension of XTAX0 is wrong by _calc_sandwidge()' assert X0TAY.shape == X0TY.shape, 'Shape of X0TAX0 is wrong by _calc_sandwidge()' + assert np.all(np.isfinite(X0TAX0_i)), 'Inverse of X0TAX0 includes NaN or Inf' ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV[idx_param_fitV['log_SNR2']], - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,False,False) + l_idx,n_C,n_T,n_V,n_run,n_base, + idx_param_fitV,n_C,False,False) vec = np.zeros(np.size(param0_fitV[idx_param_fitV['log_SNR2']])) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, False, False)[0], + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, False, False)[0], param0_fitV[idx_param_fitV['log_SNR2']], vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' # We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,True,True, + l_idx,n_C,n_T,n_V,n_run,n_base, + idx_param_fitV,n_C,True,True, dist2,inten_diff2,100,100) vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV srt log(SNR2) incorrect for model with GP' @@ -410,9 +462,12 @@ def test_gradient(): # We test the graident wrt spatial length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_space']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt spatial length scale of GP incorrect' @@ -420,9 +475,12 @@ def test_gradient(): # We test the graident wrt intensity length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_inten']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt intensity length scale of GP incorrect' @@ -430,9 +488,12 @@ def test_gradient(): # We test the graident on a random direction vec = np.random.randn(np.size(param0_fitV)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV incorrect' From cf22915c744fdf042ef5f33f18f08b91efa1a9b4 Mon Sep 17 00:00:00 2001 From: lcnature Date: Tue, 11 Oct 2016 19:48:22 -0400 Subject: [PATCH 07/30] Updated the BRSA model to incorporate spatial correlation in noise Fixed some bugs in utils.ReadDesign Renamed epsilon to eta in consistence with the paper Expanded the example a bit Other minor changes --- brainiak/reprsimil/brsa.py | 399 +++++++++++------- brainiak/utils/utils.py | 51 ++- ...tational_similarity_estimate_example.ipynb | 316 +++++++++----- tests/reprsimil/test_brsa.py | 119 +++--- tests/utils/test_utils.py | 15 +- 5 files changed, 559 insertions(+), 341 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 39b2559c1..23e41f8c0 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -63,7 +63,7 @@ class BRSA(BaseEstimator): will be provided as a quantification of neural representational similarity. .. math:: \textbf{Y = \textbf{X} \cdot \mbox{\boldmath{$\beta$}} - + \mbox{\boldmath{$\epsilon$}} + + \mbox{\boldmath{$\eta$}} .. math:: \mbox{\boldmath{$\beta$}}_i \sim \textbf{N}(0,(s_{i} \sigma_{i})^2 \textbf{U}) @@ -78,6 +78,26 @@ class BRSA(BaseEstimator): (e.g., calculating the similarity matrix of responses to each event), you might want to start with specifying a lower rank and use metrics such as AIC or BIC to decide the optimal rank. + auto_nuiance: boolean, default: True + In order to model spatial correlation between voxels that cannot + be accounted for by common response captured in the design matrix, + we assume that a set of time courses not related to the task + conditions are shared across voxels with unknown amplitudes. + One approach is for users to provide time series which they consider + as nuiance but exist in the noise (such as head motion). + The other way is to take the first n_nureg principal components + in the residual after one fitting of the Bayesian RSA model, and use + these components as the nuisance regressor. + If this flag is turned on, the nuiance regressor provided by the + user is used only in the first round of fitting. The PCs from + residuals will be used in the next round of fitting. + Note that nuiance regressor is not required from user. If it is + not provided, DC components for each run will be used as nuiance + regressor in the initial fitting. + n_nureg: int, default: 6 + Number of nuiance regressors to use in order to model signals + shared across voxels not captured by the design matrix. + This parameter will not be effective in the first round of fitting. GP_space: boolean, default: False Whether to impose a Gaussion Process (GP) prior on the log(pseudo-SNR). If true, the GP has a kernel defined over spatial coordinate. @@ -92,7 +112,7 @@ class BRSA(BaseEstimator): tol: tolerance parameter passed to the minimizer. verbose : boolean, default: False Verbose mode flag. - epsilon: a small number added to the diagonal element of the + eta: a small number added to the diagonal element of the covariance matrix in the Gaussian Process prior. This is to ensure that the matrix is invertible. space_smooth_range: the distance (in unit the same as what @@ -158,16 +178,18 @@ class BRSA(BaseEstimator): def __init__( self, n_iter=50, rank=None, GP_space=False, GP_inten=False, - tol=2e-3, verbose=False, epsilon=0.0001, - space_smooth_range=None, inten_smooth_range=None, + tol=2e-3, auto_nuiance=True, n_nureg=6, verbose=False, + eta=0.0001, space_smooth_range=None, inten_smooth_range=None, tau_range=10.0, init_iter=20, optimizer='BFGS', rand_seed=0): self.n_iter = n_iter self.rank = rank self.GP_space = GP_space self.GP_inten = GP_inten self.tol = tol + self.auto_nuiance = auto_nuiance + self.n_nureg = n_nureg self.verbose = verbose - self.epsilon = epsilon + self.eta = eta # This is a tiny ridge added to the Gaussian Process # covariance matrix template to gaurantee that it is invertible. # Mathematically it means we assume that this proportion of the @@ -185,7 +207,7 @@ def __init__( self.rand_seed = rand_seed return - def fit(self, X, design, scan_onsets=None, coords=None, + def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, inten=None): """Compute the Bayesian RSA @@ -200,16 +222,37 @@ def fit(self, X, design, scan_onsets=None, coords=None, This is the design matrix. It should only include the hypothetic response for task conditions. You do not need to include regressors for a DC component or motion parameters, unless with - a strong reason. + a strong reason. If you want to model DC component or head motion, + you should include them in nuiance regressors. + If you have multiple run, the design matrix + of all runs should be concatenated along the time dimension, + with one column across runs for each condition. + nuiance: optional, 2-D numpy array, + shape=[time_points, nuiance_factors] + The responses to these regressors will be marginalized out from + each voxel, which means they are considered, but won't be assumed + to share the same pseudo-SNR map with with the design matrix. + Therefore, the pseudo-SNR map will only reflect the + relative contribution of design matrix to each voxel. + You can provide time courses such as those for head motion + to this parameter. + Note that if auto_nuiance is set to True, this input + will only be used in the first round of fitting. The first + n_nureg principal components of residual (excluding the response + to the design matrix) will be used as the nuiance regressor + for the second round of fitting. + If auto_nuiance is set to False, the nuiance regressors supplied + by the users together with DC components will be used as + nuiance time series. scan_onsets: optional, an 1-D numpy array, shape=[runs,] - this specifies the indices of X which correspond to the onset + This specifies the indices of X which correspond to the onset of each scanning run. For example, if you have two experimental runs of the same subject, each with 100 TRs, then scan_onsets should be [0,100]. If you do not provide the argument, the program will assume all data are from the same run. - This only makes a difference for the inverse - of the temporal covariance matrix of noise. + The effect of them is to make the inverse matrix + of the temporal covariance matrix of noise block-diagonal. coords: optional, 2-D numpy array, shape=[voxels,3] This is the coordinate of each voxel, used for implementing Gaussian Process prior. @@ -253,6 +296,17 @@ def fit(self, X, design, scan_onsets=None, coords=None, assert self.rank is None or self.rank <= design.shape[1],\ 'Your design matrix has fewer columns than the rank you set' + # Check the nuiance regressors. + if nuiance is not None: + assert_all_finite(nuiance) + assert np.linalg.matrix_rank(nuiance) == nuiance.shape[1], \ + 'The nuiance regressor has rank smaller than the number of'\ + 'columns. Some columns can be explained by linear '\ + 'combination of other columns. Please check your nuiance' \ + 'regressors.' + assert np.size(nuiance, axis=0) == np.size(X, axis=0), \ + 'Nuiance regressor and data do not have the same '\ + ' number of time points.' # check scan_onsets validity assert scan_onsets is None or\ (np.max(scan_onsets) <= X.shape[0] and np.min(scan_onsets) >= 0),\ @@ -292,26 +346,32 @@ def fit(self, X, design, scan_onsets=None, coords=None, if not self.GP_space: # If GP_space is not requested, then the model is fitted # without imposing any Gaussian Process prior on log(SNR^2) - self.U_, self.L_, self.nSNR_, self.sigma_, self.rho_ = \ - self._fit_RSA_UV(X=design, Y=X, scan_onsets=scan_onsets) + self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ + self.sigma_, self.rho_ = \ + self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + scan_onsets=scan_onsets) elif not self.GP_inten: # If GP_space is requested, but GP_inten is not, a GP prior # based on spatial locations of voxels will be imposed. - self.U_, self.L_, self.nSNR_, self.sigma_, self.rho_,\ - self.lGPspace_, self.bGP_ = self._fit_RSA_UV( - X=design, Y=X, scan_onsets=scan_onsets, coords=coords) + self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ + self.sigma_, self.rho_, self.lGPspace_, self.bGP_ \ + = self._fit_RSA_UV( + X=design, Y=X, X0=nuiance, + scan_onsets=scan_onsets, coords=coords) else: # If both self.GP_space and self.GP_inten are True, # a GP prior based on both location and intensity is imposed. - self.U_, self.L_, self.nSNR_, self.sigma_, self.rho_, \ - self.lGPspace_, self.bGP_, self.lGPinten_ = \ - self._fit_RSA_UV(X=design, Y=X, scan_onsets=scan_onsets, + self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ + self.sigma_, self.rho_, self.lGPspace_, self.bGP_,\ + self.lGPinten_ = \ + self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + scan_onsets=scan_onsets, coords=coords, inten=inten) self.C_ = utils.cov2corr(self.U_) return self - # The following 2 functions below generate templates used + # The following 2 functions _D_gen and _F_gen generate templates used # for constructing inverse of covariance matrix of AR(1) noise # The inverse of covarian matrix is # (I - rho1 * D + rho1**2 * F) / sigma**2. D is a matrix where all the @@ -349,13 +409,15 @@ def _F_gen(self, TR): else: return np.empty([0, 0]) - def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): + def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): """Prepares different forms of products of design matrix X and data Y, or between themselves. These products are reused a lot during fitting. So we pre-calculate them. Because of the fact that these are reused, it is in principle possible to update the fitting as new data come in, by just incrementally adding the products of new data and their corresponding part of design matrix + no_DC means not inserting regressors for DC components into nuiance + regressor. It will only take effect if X0 is not None. """ if scan_onsets is None: # assume that all data are acquired within the same scan. @@ -408,15 +470,16 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): ' columns in your design matrix are for ' ' conditions of interest.') if X0 is not None: - res0 = np.linalg.lstsq(X_base, X0) - if not np.any(np.isclose(res0[1], 0)): - # No columns in X0 can be explained by the - # baseline regressors. So we insert them. - X0 = np.insert(X0, 0, X_base, axis=1) - else: - logger.warning('Provided regressors for non-interesting ' - 'time series already include baseline. ' - 'No additional baseline is inserted.') + if not no_DC: + res0 = np.linalg.lstsq(X_base, X0) + if not np.any(np.isclose(res0[1], 0)): + # No columns in X0 can be explained by the + # baseline regressors. So we insert them. + X0 = np.concatenate(X_base, X0, axis=1) + else: + logger.warning('Provided regressors for non-interesting ' + 'time series already include baseline. ' + 'No additional baseline is inserted.') else: # If a set of regressors for non-interested signals is not # provided, then we simply include one baseline for each run. @@ -478,9 +541,9 @@ def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, # dimension: #baseline*space X0TAX0_i = np.linalg.solve(X0TAX0, np.identity(n_base)[None, :, :]) # dimension: space*#baseline*#baseline - XTAcorrX = XTAX.copy() + XTAcorrX = XTAX # dimension: space*feature*feature - XTAcorrY = XTAY.copy() + XTAcorrY = XTAY # dimension: feature*space for i_v in range(n_V): XTAcorrX[i_v, :, :] -= \ @@ -499,9 +562,37 @@ def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, X0TAX0_i, X0TAY), axis=0) # dimension: space - return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + return X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL + def _calc_LL(self, rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, SNR2, + n_V, n_T, n_run, rank, n_base): + # Calculate the log likelihood (excluding the GP prior of log(SNR)) + # for both _loglike_AR1_diagV_fitU and _loglike_AR1_diagV_fitV, + # in addition to a few other terms. + LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) + # dimension: space*rank*rank + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) + # dimension: space*rank*rank + # LAMBDA is essentially the inverse covariance matrix of the + # posterior probability of alpha, which bears the relation with + # beta by beta = L * alpha. L is the Cholesky factor of the + # shared covariance matrix U. Refer to the explanation below + # Equation 5 in the NIPS paper. + + YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) + # dimension: space*rank + sigma2 = (YTAcorrY - np.sum(LTXTAcorrY * YTAcorrXL_LAMBDA.T, axis=0) + * SNR2) / (n_T - n_base) + # dimension: space + LL = - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5 \ + + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ + - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5 \ + - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ + - (n_T - n_base) * n_V * (1 + np.log(2 * np.pi)) * 0.5 + # Log likelihood + return LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 + def _calc_dist2_GP(self, coords=None, inten=None, GP_space=False, GP_inten=False): # calculate the square of difference between each voxel's location @@ -562,7 +653,7 @@ def _build_index_param(self, n_l, n_V, n_smooth): # each voxel) return idx_param_sing, idx_param_fitU, idx_param_fitV - def _fit_RSA_UV(self, X, Y, + def _fit_RSA_UV(self, X, Y, X0, scan_onsets=None, coords=None, inten=None): """ The major utility of fitting Bayesian RSA. Note that there is a naming change of variable. X in fit() @@ -612,10 +703,13 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets) + = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + X0=X0, no_DC=False) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and # gradient. + # DC component will be added to the nuiance regressors. + # In later steps, we do not need to add DC components again dist2, inten_diff2, space_smooth_range, inten_smooth_range,\ n_smooth = self._calc_dist2_GP( @@ -651,7 +745,7 @@ def _fit_RSA_UV(self, X, Y, # as the number of iteration. # Step 1 fitting, with a simplified model - current_vec_U_chlsk_l_AR1, current_a1, current_logSigma2 = \ + current_vec_U_chlsk_l, current_a1, current_logSigma2 = \ self._initial_fit_singpara( XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, @@ -662,18 +756,16 @@ def _fit_RSA_UV(self, X, Y, current_logSNR2 = -current_logSigma2 norm_factor = np.mean(current_logSNR2) current_logSNR2 = current_logSNR2 - norm_factor - # current_vec_U_chlsk_l_AR1 = current_vec_U_chlsk_l_AR1 \ - # * np.exp(norm_factor / 2.0) # Step 2 fitting, which only happens if # GP prior is requested if GP_space: - current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 \ + current_vec_U_chlsk_l, current_a1, current_logSNR2 \ = self._fit_diagV_noGP( XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank) @@ -701,32 +793,39 @@ def _fit_RSA_UV(self, X, Y, # many voxels have close to equal intensities, # which might render 5 percential to 0. - # Step 3 fitting. + # Step 3 fitting. GP prior is imposed if requested. + # In this step, unless auto_nuiance is set to False, X0 + # will be re-estimated from the residuals after each step + # of fitting. logger.debug('indexing:{}'.format(idx_param_fitV)) logger.debug('initial GP parameters:{}'.format(current_GP)) - current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2,\ - current_GP = self._fit_diagV_GP( - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, current_logSNR2,\ + current_GP, X0 = self._fit_diagV_GP( + X, Y, scan_onsets, X0, + current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range) - logger.debug('final GP parameters:{}'.format(current_GP)) estU_chlsk_l_AR1_UV = np.zeros([n_C, rank]) - estU_chlsk_l_AR1_UV[l_idx] = current_vec_U_chlsk_l_AR1 + estU_chlsk_l_AR1_UV[l_idx] = current_vec_U_chlsk_l est_cov_AR1_UV = np.dot(estU_chlsk_l_AR1_UV, estU_chlsk_l_AR1_UV.T) est_rho1_AR1_UV = 2 / np.pi * np.arctan(current_a1) est_SNR_AR1_UV = np.exp(current_logSNR2 / 2.0) - # Calculating est_sigma_AR1_UV - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + # Calculating est_sigma_AR1_UV, est_sigma_AR1_UV, + # est_beta_AR1_UV and est_beta0_AR1_UV + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_run, n_base \ + = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + X0=X0, no_DC=True) + + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL\ = self._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, @@ -734,20 +833,21 @@ def _fit_RSA_UV(self, X, Y, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, estU_chlsk_l_AR1_UV, est_rho1_AR1_UV, n_V, n_base) - LAMBDA_i = LTXTAcorrXL * est_SNR_AR1_UV[:, None, None]**2 \ - + np.eye(rank) - # dimension: space*rank*rank - LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) - # dimension: space*rank*rank - YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) - # dimension: space*rank - est_sigma_AR1_UV = ((YTAcorrY - np.sum(LTXTAcorrY - * YTAcorrXL_LAMBDA.T, axis=0) - * est_SNR_AR1_UV**2) / (n_T - n_base)) ** 0.5 + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(est_rho1_AR1_UV, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, est_SNR_AR1_UV**2, + n_V, n_T, n_run, rank, n_base) + est_sigma_AR1_UV = sigma2**0.5 + est_beta_AR1_UV = est_sigma_AR1_UV * est_SNR_AR1_UV**2 \ + * np.dot(estU_chlsk_l_AR1_UV, YTAcorrXL_LAMBDA.T) + est_beta0_AR1_UV = np.einsum( + 'ijk,ki->ji', X0TAX0_i, + (X0TAY - np.einsum('ikj,ki->ji', XTAX0, est_beta_AR1_UV))) t_finish = time.time() logger.info( 'total time of fitting: {} seconds'.format(t_finish - t_start)) + logger.debug('final GP parameters:{}'.format(current_GP)) if GP_space: est_space_smooth_r = np.exp(current_GP[0] / 2.0) if GP_inten: @@ -755,25 +855,28 @@ def _fit_RSA_UV(self, X, Y, K_major = np.exp(- (dist2 / est_space_smooth_r**2 + inten_diff2 / est_intensity_kernel_r**2) / 2.0) - K = K_major + np.diag(np.ones(n_V) * self.epsilon) + K = K_major + np.diag(np.ones(n_V) * self.eta) est_std_log_SNR = (np.dot(current_logSNR2, np.dot( np.linalg.inv(K), current_logSNR2)) / n_V / 4)**0.5 # divided by 4 because we used # log(SNR^2) instead of log(SNR) return est_cov_AR1_UV, estU_chlsk_l_AR1_UV, est_SNR_AR1_UV, \ - est_sigma_AR1_UV, est_rho1_AR1_UV, est_space_smooth_r, \ + est_beta_AR1_UV, est_beta0_AR1_UV, est_sigma_AR1_UV, \ + est_rho1_AR1_UV, est_space_smooth_r, \ est_std_log_SNR, est_intensity_kernel_r # When GP_inten is True, the following lines won't be reached else: K_major = np.exp(- dist2 / est_space_smooth_r**2 / 2.0) - K = K_major + np.diag(np.ones(n_V) * self.epsilon) + K = K_major + np.diag(np.ones(n_V) * self.eta) est_std_log_SNR = (np.dot(current_logSNR2, np.dot( np.linalg.inv(K), current_logSNR2)) / n_V / 4)**0.5 return est_cov_AR1_UV, estU_chlsk_l_AR1_UV, est_SNR_AR1_UV, \ + est_beta_AR1_UV, est_beta0_AR1_UV, \ est_sigma_AR1_UV, est_rho1_AR1_UV, est_space_smooth_r, \ est_std_log_SNR else: return est_cov_AR1_UV, estU_chlsk_l_AR1_UV, est_SNR_AR1_UV, \ + est_beta_AR1_UV, est_beta0_AR1_UV, \ est_sigma_AR1_UV, est_rho1_AR1_UV def _initial_fit_singpara(self, XTX, XTDX, XTFX, @@ -800,7 +903,7 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, # (1) start from the point estimation of covariance # cov_point_est = np.cov(beta_hat) - # current_vec_U_chlsk_l_AR1 = \ + # current_vec_U_chlsk_l = \ # np.linalg.cholesky(cov_point_est + \ # np.eye(n_C) * 1e-6)[l_idx] @@ -811,11 +914,11 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, # (2) start from identity matrix - # current_vec_U_chlsk_l_AR1 = np.eye(n_C)[l_idx] + # current_vec_U_chlsk_l = np.eye(n_C)[l_idx] # (3) random initialization - current_vec_U_chlsk_l_AR1 = np.random.randn(n_l) + current_vec_U_chlsk_l = np.random.randn(n_l) # vectorized version of L, Cholesky factor of U, the shared # covariance matrix of betas across voxels. @@ -831,9 +934,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, for v in idx_param_sing.values())) # Initial parameter # Then we fill each part of the original guess of parameters - param0[idx_param_sing['Cholesky']] = current_vec_U_chlsk_l_AR1 + param0[idx_param_sing['Cholesky']] = current_vec_U_chlsk_l param0[idx_param_sing['a1']] = np.median(np.tan(rho1 * np.pi / 2)) - # param0[idx_param_sing['log_sigma2']] = np.median(log_sigma2) # Fit it. res = scipy.optimize.minimize( @@ -845,26 +947,26 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, options={'disp': self.verbose, 'maxiter': 100}) - current_vec_U_chlsk_l_AR1 = res.x[idx_param_sing['Cholesky']] + current_vec_U_chlsk_l = res.x[idx_param_sing['Cholesky']] current_a1 = res.x[idx_param_sing['a1']] * np.ones(n_V) # log(sigma^2) assuming the data include no signal is returned, # as a starting point for the iteration in the next step. # Although it should overestimate the variance, # setting it this way might allow it to track log(sigma^2) # more closely for each voxel. - return current_vec_U_chlsk_l_AR1, current_a1, log_sigma2 + return current_vec_U_chlsk_l, current_a1, log_sigma2 def _fit_diagV_noGP( self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank): """ (optional) second step of fitting, full model but without - GP prior on log(SNR). This is only used when GP is - requested. + GP prior on log(SNR). This step is only done if GP prior + is requested. """ init_iter = self.init_iter logger.info('second fitting without GP prior' @@ -877,7 +979,7 @@ def _fit_diagV_noGP( # We cannot use the same logic as the line above because # idx_param_fitV also includes entries for GP parameters. param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1.copy() + current_vec_U_chlsk_l.copy() param0_fitU[idx_param_fitU['a1']] = current_a1.copy() param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() @@ -886,9 +988,14 @@ def _fit_diagV_noGP( tol = self.tol * 5 for it in range(0, init_iter): # fit V, reflected in the log(SNR^2) of each voxel + # XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + # XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + # X0TY, X0TDY, X0TFY, X0, n_run, n_base \ + # = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + # X0=X0) rho1 = np.arctan(current_a1) * 2 / np.pi - L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + L[l_idx] = current_vec_U_chlsk_l + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, \ LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, @@ -900,10 +1007,10 @@ def _fit_diagV_noGP( L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, - args=(XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + args=(X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitV, rank, False, False), @@ -933,7 +1040,7 @@ def _fit_diagV_noGP( # fit U, the covariance matrix, together with AR(1) param param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1 + current_vec_U_chlsk_l param0_fitU[idx_param_fitU['a1']] = current_a1 res_fitU = scipy.optimize.minimize( self._loglike_AR1_diagV_fitU, param0_fitU, @@ -945,7 +1052,7 @@ def _fit_diagV_noGP( method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 3}) - current_vec_U_chlsk_l_AR1 = \ + current_vec_U_chlsk_l = \ res_fitU.x[idx_param_fitU['Cholesky']] current_a1 = res_fitU.x[idx_param_fitU['a1']] norm_fitUchange = np.linalg.norm(res_fitU.x - param0_fitU) @@ -957,19 +1064,17 @@ def _fit_diagV_noGP( and norm_fitUchange / np.sqrt(param0_fitU.size) \ < tol: break - return current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 + return current_vec_U_chlsk_l, current_a1, current_logSNR2 def _fit_diagV_GP( - self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + self, X, Y, scan_onsets, X0, + current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range): - """ Last step of fitting. If GP is not requested, it will still - fit. + """ Last step of fitting. If GP is not requested, this step will + still be done, just without GP prior on log(SNR). """ tol = self.tol n_iter = self.n_iter @@ -984,23 +1089,24 @@ def _fit_diagV_GP( # We cannot use the same logic as the line above because # idx_param_fitV also includes entries for GP parameters. param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1.copy() + current_vec_U_chlsk_l.copy() param0_fitU[idx_param_fitU['a1']] = current_a1.copy() param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() L = np.zeros((n_C, rank)) + L[l_idx] = current_vec_U_chlsk_l if self.GP_space: param0_fitV[idx_param_fitV['c_both']] = current_GP.copy() - # param0_fitV[idx_param_fitV['c_space']] = \ - # current_GP[0] - # if self.GP_inten: - # param0_fitV[idx_param_fitV['c_inten']] = \ - # current_GP[1] + for it in range(0, n_iter): + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_run, n_base \ + = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + X0=X0, no_DC=True) # fit V rho1 = np.arctan(current_a1) * 2 / np.pi - L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, \ LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, @@ -1012,17 +1118,17 @@ def _fit_diagV_GP( L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=( - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, + X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, - current_vec_U_chlsk_l_AR1, current_a1, + current_vec_U_chlsk_l, current_a1, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitV, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range), method=self.optimizer, jac=True, - tol=tol, # 10**(-2 - 2 / n_iter * (it + 1)), - options={'xtol': tol, # 10**(-3 - 3 / n_iter * (it + 1)), + tol=tol, + options={'xtol': tol, 'disp': self.verbose, 'maxiter': 6}) current_logSNR2[0:n_V - 1] = \ @@ -1042,7 +1148,7 @@ def _fit_diagV_GP( # fit U param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1 + current_vec_U_chlsk_l param0_fitU[idx_param_fitU['a1']] = current_a1 res_fitU = scipy.optimize.minimize( @@ -1056,17 +1162,30 @@ def _fit_diagV_GP( tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 6}) - current_vec_U_chlsk_l_AR1 = \ + current_vec_U_chlsk_l = \ res_fitU.x[idx_param_fitU['Cholesky']] current_a1 = res_fitU.x[idx_param_fitU['a1']] - + L[l_idx] = current_vec_U_chlsk_l fitUchange = res_fitU.x - param0_fitU norm_fitUchange = np.linalg.norm(fitUchange) logger.debug('norm of parameter change after fitting U: ' '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() - # Debugging purpose. But it exceeds complexity limit + current_SNR2 = np.exp(current_logSNR2) + + # Re-estimating X0 from residuals + if self.auto_nuiance: + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, current_sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, current_SNR2, + n_V, n_T, n_run, rank, n_base) + betas = current_sigma2**0.5 * current_SNR2 \ + * np.dot(L, YTAcorrXL_LAMBDA.T) + residuals = Y - np.dot(X, betas) + u, s, v = np.linalg.svd(residuals) + X0 = u[:, :self.n_nureg] + if GP_space: logger.debug('current GP[0]: {}'.format(current_GP[0])) logger.debug('gradient for GP[0]: {}'.format( @@ -1079,8 +1198,8 @@ def _fit_diagV_GP( np.max(np.abs(fitUchange)) < tol: break - return current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2,\ - current_GP + return current_vec_U_chlsk_l, current_a1, current_logSNR2,\ + current_GP, X0 # We fit two parts of the parameters iteratively. # The following are the corresponding negative log likelihood functions. @@ -1132,7 +1251,7 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # each element of SNR2 is the ratio of the diagonal element on V # to the variance of the fresh noise in that voxel - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, \ LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, @@ -1142,35 +1261,16 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, L, rho1, n_V, n_base) # Only starting from this point, SNR2 is involved - LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) - # dimension: space*rank*rank - LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) - # dimension: space*rank*rank - # LAMBDA is essentially the inverse covariance matrix of the - # posterior probability of alpha, which bears the relation with - # beta by beta = L * alpha, and L is the Cholesky factor of the - # shared covariance matrix U. refer to the explanation below - # Equation 5 in the NIPS paper. - - # LAMBDA_LTXTAcorrY = np.einsum('ijk,ki->ji', LAMBDA_i, LTXTAcorrY) - YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) - # dimension: space*rank - # # dimension: feature*space - sigma2 = (YTAcorrY - np.sum(LTXTAcorrY * YTAcorrXL_LAMBDA.T, axis=0) - * SNR2) / (n_T - n_base) - - LL = - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5 \ - + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ - - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5 \ - - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ - - (n_T - n_base) * n_V * (1 + np.log(2 * np.pi)) * 0.5 + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, + SNR2, n_V, n_T, n_run, rank, n_base) if not np.isfinite(LL): - print('NaN detected!') - print(sigma2) - print(YTAcorrY) - print(LTXTAcorrY) - print(YTAcorrXL_LAMBDA) - print(SNR2) + logger.debug('NaN detected!') + logger.debug(sigma2) + logger.debug(YTAcorrY) + logger.debug(LTXTAcorrY) + logger.debug(YTAcorrXL_LAMBDA) + logger.debug(SNR2) YTAcorrXL_LAMBDA_LT = np.dot(YTAcorrXL_LAMBDA, L.T) # dimension: space*feature (feature can be larger than rank) @@ -1240,13 +1340,13 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, dXTAcorrX_drho1_ele), YTAcorrXL_LAMBDA_LT[i_v, :])) - deriv = np.zeros(np.size(param)) + deriv = np.empty(np.size(param)) deriv[idx_param_fitU['Cholesky']] = deriv_L[l_idx] deriv[idx_param_fitU['a1']] = deriv_a1 return -LL, -deriv - def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, + def _loglike_AR1_diagV_fitV(self, param, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, @@ -1303,24 +1403,9 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # If requested, a GP prior is imposed on log(SNR). rho1 = 2.0 / np.pi * np.arctan(a1) # AR(1) coefficient, dimension: space - LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) - - # dimension: space*rank*rank - LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) - # dimension: space*rank*rank - YTAcorrXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAcorrY) - # dimension: space*rank - sigma2 = (YTAcorrY - - SNR2 * np.sum(YTAcorrXL_LAMBDA - * LTXTAcorrY.T, axis=1)) / (n_T - n_base) - # dimension: space - - LL = - (n_T - n_base) * np.log(2 * np.pi) * 0.5\ - - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5\ - + np.sum(np.log(1 - rho1**2)) * n_run * 0.5\ - - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5\ - - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5\ - - (n_T - n_base) * n_V * 0.5 + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, + SNR2, n_V, n_T, n_run, rank, n_base) # Log likelihood of data given parameters, without the GP prior. deriv_log_SNR2 = (-rank + np.trace(LAMBDA, axis1=1, axis2=2)) * 0.5\ + YTAcorrY / (sigma2 * 2.0) - (n_T - n_base) * 0.5 \ @@ -1356,7 +1441,7 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # The kernel defined over the spatial coordinates of voxels. # This is a template: the diagonal values are all 1, meaning # the variance of log(SNR) has not been multiplied - K_tilde = K_major + np.diag(np.ones(n_V) * self.epsilon) + K_tilde = K_major + np.diag(np.ones(n_V) * self.eta) # We add a small number to the diagonal to make sure the matrix # is invertible. # Note that the K_tilder here is still template: @@ -1435,7 +1520,7 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # the magnitude of log(SNR). deriv_log_SNR2 += - log_SNR2 / self.tau_range**2 / 4.0 - deriv = np.zeros(np.size(param)) + deriv = np.empty(np.size(param)) deriv[idx_param_fitV['log_SNR2']] = \ deriv_log_SNR2[0:n_V - 1] - deriv_log_SNR2[n_V - 1] if GP_space: @@ -1544,7 +1629,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, - 0.5 * np.sum(np.dot(dXTAcorrX_drho1, L_LAMBDA_LTXTAcorrY) * L_LAMBDA_LTXTAcorrY) / sigma2) - deriv = np.zeros(np.size(param)) + deriv = np.empty(np.size(param)) deriv[idx_param_sing['Cholesky']] = deriv_L[l_idx] deriv[idx_param_sing['a1']] = deriv_a1 diff --git a/brainiak/utils/utils.py b/brainiak/utils/utils.py index 44b9bbc37..ed73bd1ec 100644 --- a/brainiak/utils/utils.py +++ b/brainiak/utils/utils.py @@ -138,20 +138,25 @@ class ReadDesign: fname: string, the address of the file to read. include_orth: Boollean, whether to include "orthogonal" regressors in - the design matrix which are usually head motion parameters. All - the columns of design matrix are still going to be read in, but - the attribute cols_used will reflect whether these orthogonal + the nuisance regressors which are usually head motion parameters. + All the columns of design matrix are still going to be read in, + but the attribute cols_used will reflect whether these orthogonal regressors are to be included for furhter analysis. + Note that these are not entered into design_task attribute which + include only regressors related to task conditions. include_pols: Boollean, whether to include polynomial regressors in - the design matrix which are used to capture slow drift of signals. - This will be reflected in the indices in the attribute cols_used. + the nuisance regressors which are used to capture slow drift of + signals. Attributes ---------- design: 2d array. The design matrix read in from the csv file. + design_task: 2d array. The part of design matrix corresponding to + task conditions. + n_col: number of total columns in the design matrix. column_types: 1d array. the types of each column in the design matrix. @@ -168,7 +173,7 @@ class ReadDesign: StimLabels: list. The names of each column in the design matrix. """ - def __init__(self, fname=None, include_orth=False, include_pols=False): + def __init__(self, fname=None, include_orth=True, include_pols=True): if fname is None: # fname is the name of the file to read in the design matrix self.design = np.zeros([0, 0]) @@ -188,18 +193,32 @@ def __init__(self, fname=None, include_orth=False, include_pols=False): self.include_orth = include_orth self.include_pols = include_pols - self.cols_used = np.where(self.column_types == 1)[0] + # The two flags above dictates whether columns corresponding to + # baseline drift modeled by polynomial functions of time and + # columns corresponding to other orthogonal signals (usually motion) + # are included in nuisance regressors. + self.cols_task = np.where(self.column_types == 1)[0] + self.design_task = self.design[:, self.cols_task] + if np.ndim(self.design_task) == 1: + self.design_task = self.design_task[:, None] + # part of the design matrix related to task conditions. + self.n_TR = np.size(self.design_task, axis=0) + self.cols_nuisance = np.array([]) if self.include_orth: - self.cols_used = np.sort( - np.append(self.cols_used, np.where(self.column_types == 0)[0])) + self.cols_nuisance = np.int0( + np.sort(np.append(self.cols_nuisance, + np.where(self.column_types == 0)[0]))) if self.include_pols: - self.cols_used = np.sort(np.append( - self.cols_used, np.where(self.column_types == -1)[0])) - self.design_used = self.design[:, self.cols_used] - if not self.include_pols: - # baseline is not included, then we add a column of all 1's - self.design_used = np.insert(self.design_used, 0, 1, axis=1) - self.n_TR = np.size(self.design_used, axis=0) + self.cols_nuisance = np.int0( + np.sort(np.append(self.cols_nuisance, + np.where(self.column_types == -1)[0]))) + if np.size(self.cols_nuisance) > 0: + self.reg_nuisance = self.design[:, self.cols_nuisance] + if np.ndim(self.reg_nuisance) == 1: + self.reg_nuisance = self.reg_nuisance[:, None] + else: + self.reg_nuisance = None + # Nuisance regressors for motion, baseline, etc. def read_afni(self, fname): # Read design file written by AFNI diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 187727706..e78329a4f 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -1,12 +1,10 @@ { "cells": [ { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "collapsed": false }, - "outputs": [], "source": [ "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset." ] @@ -54,15 +52,17 @@ }, "outputs": [], "source": [ - "logging.basicConfig(level=logging.DEBUG, filename='brsa_example.log',\n", - " format='%(relativeCreated)6d %(threadName)s %(message)s')" + "logging.basicConfig(\n", + " level=logging.DEBUG,\n", + " filename='brsa_example.log',\n", + " format='%(relativeCreated)6d %(threadName)s %(message)s')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# (1) We want to simulate some data in which each voxel respond to different task conditions differently, but following a common covariance structure" + "# We want to simulate some data in which each voxel responds to different task conditions differently, but following a common covariance structure" ] }, { @@ -93,27 +93,33 @@ "design = utils.ReadDesign(fname=\"example_design.1D\")\n", "\n", "n_run = 2\n", - "design.design_used = np.tile(design.design_used[:,1:17],[n_run,1])\n", "design.n_TR = design.n_TR * n_run\n", - "\n", - "\n", - "fig = plt.figure(num=None, figsize=(12, 3), dpi=150, facecolor='w', edgecolor='k')\n", - "\n", - "plt.plot(design.design_used)\n", - "plt.ylim([-0.2,0.4])\n", - "plt.title('hypothetic fMRI response time courses of all conditions in addition to a DC component\\n'\n", + "design.design_task = np.tile(design.design_task[:,:-1],\n", + " [n_run, 1])\n", + "# The last \"condition\" in design matrix\n", + "# codes for trials subjects made and error.\n", + "# We ignore it here.\n", + "\n", + "\n", + "fig = plt.figure(num=None, figsize=(12, 3),\n", + " dpi=150, facecolor='w', edgecolor='k')\n", + "plt.plot(design.design_task)\n", + "plt.ylim([-0.2, 0.4])\n", + "plt.title('hypothetic fMRI response time courses '\n", + " 'of all conditions in addition to a DC component\\n'\n", " '(design matrix)')\n", "plt.xlabel('time')\n", "plt.show()\n", "\n", - "n_C = np.size(design.design_used,axis=1) \n", + "n_C = np.size(design.design_task, axis=1)\n", "# The total number of conditions.\n", - "ROI_edge = 25\n", + "ROI_edge = 20\n", "# We simulate \"ROI\" of a square shape\n", "n_V = ROI_edge**2\n", "# The total number of simulated voxels\n", "n_T = design.n_TR\n", - "# The total number of time points, after concatenating all fMRI runs\n" + "# The total number of time points,\n", + "# after concatenating all fMRI runs\n" ] }, { @@ -121,7 +127,7 @@ "metadata": {}, "source": [ "## simulate data: noise + signal\n", - "### First, we start with noise" + "### First, we start with noise, which is Gaussian Process in space and AR(1) in time" ] }, { @@ -134,7 +140,8 @@ "source": [ "noise_bot = 0.5\n", "noise_top = 1.5\n", - "noise_level = np.random.rand(n_V)*(noise_top-noise_bot)+noise_bot\n", + "noise_level = np.random.rand(n_V) * \\\n", + " (noise_top - noise_bot) + noise_bot\n", "# The standard deviation of the noise is in the range of [noise_bot, noise_top]\n", "# In fact, we simulate autocorrelated noise with AR(1) model. So the noise_level reflects\n", "# the independent additive noise at each time point (the \"fresh\" noise)\n", @@ -142,18 +149,44 @@ "# AR(1) coefficient\n", "rho1_top = 0.8\n", "rho1_bot = -0.2\n", - "rho1 = np.random.rand(n_V)*(rho1_top-rho1_bot)+rho1_bot\n", + "rho1 = np.random.rand(n_V) \\\n", + " * (rho1_top - rho1_bot) + rho1_bot\n", + "\n", "\n", + "noise_smooth_width = 10.0\n", + "coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", + "coords_flat = np.reshape(coords,[3, n_V]).T\n", + "dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", "\n", "# generating noise\n", - "noise = np.zeros([n_T,n_V])\n", - "noise[0,:] = np.random.randn(n_V) * noise_level / np.sqrt(1-rho1**2)\n", - "for i_t in range(1,n_T):\n", - " noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", + "K_noise = noise_level[:, np.newaxis] \\\n", + " * (np.exp(-dist2 / noise_smooth_width**2 / 2.0) \\\n", + " + np.eye(n_V) * 0.1) * noise_level\n", + "print(np.shape(K_noise))\n", + "plt.pcolor(K_noise)\n", + "plt.colorbar()\n", + "plt.xlim([0, ROI_edge * ROI_edge])\n", + "plt.ylim([0, ROI_edge * ROI_edge])\n", + "plt.title('Spatial covariance matrix of noise')\n", + "plt.show()\n", + "L_noise = np.linalg.cholesky(K_noise)\n", + "noise = np.zeros([n_T, n_V])\n", + "noise[0, :] = np.dot(L_noise, np.random.randn(n_V))\\\n", + " / np.sqrt(1 - rho1**2)\n", + "for i_t in range(1, n_T):\n", + " noise[i_t, :] = noise[i_t - 1, :] * rho1 \\\n", + " + np.dot(L_noise,np.random.randn(n_V))\n", + "\n", + "\n", + "# noise = np.zeros([n_T,n_V])\n", + "# noise[0,:] = np.random.randn(n_V) * noise_level / np.sqrt(1-rho1**2)\n", + "# for i_t in range(1,n_T):\n", + "# noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", "# Here, we assume noise is independent between voxels\n", "noise = noise + np.random.randn(n_V)\n", - "fig = plt.figure(num=None, figsize=(12, 2), dpi=150, facecolor='w', edgecolor='k')\n", - "plt.plot(noise[:,0])\n", + "fig = plt.figure(num=None, figsize=(12, 2), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", + "plt.plot(noise[:, 0])\n", "plt.title('noise in an example voxel')\n", "plt.show()" ] @@ -162,7 +195,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Then, we simulate signals, assuming the magnitude of response to each condition follows a common covariance matrix\n", + "### Then, we simulate signals, assuming the magnitude of response to each condition follows a common covariance matrix. \n", "#### Our model allows to impose a Gaussian Process prior on the log(SNR) of each voxels. \n", "What this means is that SNR turn to be smooth and local, but betas (response amplitudes of each voxel to each condition) are not necessarily correlated in space. Intuitively, this is based on the assumption that voxels coding for related aspects of a task turn to be clustered (instead of isolated)\n", "\n", @@ -177,7 +210,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "##### Note: the following code won't work if you just installed Brainiak. It serves as an example for you to retrieve coordinates of voxels in an ROI. You can use the ROI_coords for the argument coords in BRSA.fit()" + "##### Note: the following code won't work if you just installed Brainiak and try this demo because ROI.nii does not exist. It just serves as an example for you to retrieve coordinates of voxels in an ROI. You can use the ROI_coords for the argument coords in BRSA.fit()" ] }, { @@ -192,10 +225,11 @@ "# ROI = nibabel.load('ROI.nii')\n", "# I,J,K = ROI.shape \n", "# all_coords = np.zeros((I, J, K, 3)) \n", - "# all_coords[...,0] = np.arange(I)[:,np.newaxis,np.newaxis] \n", - "# all_coords[...,1] = np.arange(J)[np.newaxis,:,np.newaxis] \n", - "# all_coords[...,2] = np.arange(K)[np.newaxis,np.newaxis,:] \n", - "# ROI_coords = nibabel.affines.apply_affine(ROI.affine, all_coords[ROI.get_data().astype(bool)])\n" + "# all_coords[...,0] = np.arange(I)[:, np.newaxis, np.newaxis] \n", + "# all_coords[...,1] = np.arange(J)[np.newaxis, :, np.newaxis] \n", + "# all_coords[...,2] = np.arange(K)[np.newaxis, np.newaxis, :] \n", + "# ROI_coords = nibabel.affines.apply_affine(\n", + "# ROI.affine, all_coords[ROI.get_data().astype(bool)])\n" ] }, { @@ -214,29 +248,29 @@ "outputs": [], "source": [ "# ideal covariance matrix\n", - "ideal_cov = np.zeros([n_C,n_C])\n", - "ideal_cov = np.eye(n_C)*0.6\n", - "ideal_cov[8:12,8:12] = 0.8\n", - "for cond in range(8,12):\n", + "ideal_cov = np.zeros([n_C, n_C])\n", + "ideal_cov = np.eye(n_C) * 0.6\n", + "ideal_cov[8:12, 8:12] = 0.8\n", + "for cond in range(8, 12):\n", " ideal_cov[cond,cond] = 1\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_cov)\n", "plt.colorbar()\n", - "plt.xlim([0,16])\n", - "plt.ylim([0,16])\n", + "plt.xlim([0, 16])\n", + "plt.ylim([0, 16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal covariance matrix')\n", "plt.show()\n", "\n", "std_diag = np.diag(ideal_cov)**0.5\n", - "ideal_corr = ideal_cov / std_diag / std_diag[:,None]\n", + "ideal_corr = ideal_cov / std_diag / std_diag[:, None]\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_corr)\n", "plt.colorbar()\n", - "plt.xlim([0,16])\n", - "plt.ylim([0,16])\n", + "plt.xlim([0, 16])\n", + "plt.ylim([0, 16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal correlation matrix')\n", @@ -247,7 +281,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### In the following, pseudo-SNR is generated from a Gaussian process defined on a \"linear\" ROI, just for simplicity of code" + "#### In the following, pseudo-SNR is generated from a Gaussian Process defined on a \"square\" ROI, just for simplicity of code" ] }, { @@ -258,16 +292,15 @@ }, "outputs": [], "source": [ - "\n", - "\n", "L_full = np.linalg.cholesky(ideal_cov) \n", "\n", "# generating signal\n", "snr_level = 0.6\n", - "# Notice that accurately speaking this is not snr. the magnitude of signal depends\n", - "# not only on beta but also on x. (noise_level*snr_level)**2 is the factor multiplied\n", - "# with ideal_cov to form the covariance matrix from which the response amplitudes (beta)\n", - "# of a voxel are drawn from.\n", + "# Notice that accurately speaking this is not SNR.\n", + "# The magnitude of signal depends not only on beta but also on x.\n", + "# (noise_level*snr_level)**2 is the factor multiplied\n", + "# with ideal_cov to form the covariance matrix from which\n", + "# the response amplitudes (beta) of a voxel are drawn from.\n", "\n", "tau = 0.8\n", "# magnitude of Gaussian Process from which the log(SNR) is drawn\n", @@ -280,12 +313,13 @@ "# then the smoothness has much small dependency on the intensity.\n", "\n", "\n", - "coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", - "coords_flat = np.reshape(coords,[3, n_V]).T\n", - "dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", + "# coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", + "# coords_flat = np.reshape(coords,[3, n_V]).T\n", + "# dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", "\n", "inten = np.random.rand(n_V) * 20.0\n", - "# For simplicity, we just assume that the intensity of all voxels are uniform distributed between 0 and 20\n", + "# For simplicity, we just assume that the intensity\n", + "# of all voxels are uniform distributed between 0 and 20\n", "# parameters of Gaussian process to generate pseuso SNR\n", "# For curious user, you can also try the following commond\n", "# to see what an example snr map might look like if the intensity\n", @@ -294,34 +328,39 @@ "# inten = coords_flat[:,0] * 2\n", "\n", "\n", - "inten_tile = np.tile(inten,[n_V,1])\n", - "inten_diff2 = (inten_tile-inten_tile.T)**2\n", + "inten_tile = np.tile(inten, [n_V, 1])\n", + "inten_diff2 = (inten_tile - inten_tile.T)**2\n", "\n", - "K = np.exp(-dist2/smooth_width**2/2.0 -inten_diff2/inten_kernel**2/2.0) * tau**2 \\\n", - " + np.eye(n_V)*tau**2*0.001\n", - "# A tiny amount is added to the diagonal of the GP covariance matrix to make sure it can be inverted\n", + "K = np.exp(-dist2 / smooth_width**2 / 2.0 \n", + " - inten_diff2 / inten_kernel**2 / 2.0) * tau**2 \\\n", + " + np.eye(n_V) * tau**2 * 0.001\n", + "# A tiny amount is added to the diagonal of\n", + "# the GP covariance matrix to make sure it can be inverted\n", "L = np.linalg.cholesky(K)\n", - "snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level\n", - "sqrt_v = noise_level*snr\n", - "betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v\n", - "signal = np.dot(design.design_used,betas_simulated)\n", + "snr = np.exp(np.dot(L, np.random.randn(n_V))) * snr_level\n", + "sqrt_v = noise_level * snr\n", + "betas_simulated = np.dot(L_full, np.random.randn(n_C, n_V)) * sqrt_v\n", + "signal = np.dot(design.design_task, betas_simulated)\n", "\n", "\n", "Y = signal + noise \n", "# The data to be fed to the program.\n", "\n", "\n", - "idx = np.argmin(np.abs(snr-np.median(snr)))\n", + "idx = np.argmin(np.abs(snr - np.median(snr)))\n", "# choose a voxel of medium level SNR.\n", - "fig = plt.figure(num=None, figsize=(12, 4), dpi=150, facecolor='w', edgecolor='k')\n", + "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", "noise_plot, = plt.plot(noise[:,idx],'g')\n", "signal_plot, = plt.plot(signal[:,idx],'r')\n", "plt.legend([noise_plot, signal_plot], ['noise', 'signal'])\n", - "plt.title('simulated data in an example voxel with pseudo-SNR of {}'.format(snr[idx]))\n", + "plt.title('simulated data in an example voxel'\n", + " ' with pseudo-SNR of {}'.format(snr[idx]))\n", "plt.xlabel('time')\n", "plt.show()\n", "\n", - "fig = plt.figure(num=None, figsize=(12, 4), dpi=150, facecolor='w', edgecolor='k')\n", + "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", "data_plot, = plt.plot(Y[:,idx],'b')\n", "plt.legend([data_plot], ['observed data'])\n", "plt.xlabel('time')\n", @@ -332,7 +371,7 @@ "plt.colorbar()\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", - "plt.title('pseudo-SNR')\n", + "plt.title('pseudo-SNR in a square \"ROI\"')\n", "plt.show()" ] }, @@ -340,14 +379,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### The reason that the pseudo-SNR in the example voxel is not too small, while the signal looks much smaller is because we happen to have low amplitudes in our design matrix. The True SNR depends on both the amplitudes in design matrix and the pseudo-SNR. Therefore, be aware that pseudo-SNR does not directly reflects how much signal the data have, but rather a map indicating the relative strength of signal in differerent voxels." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### When you have multiple runs, the noise won't be correlated between runs. Therefore, you should tell BRSA when is the onset of each scan" + "#### The reason that the pseudo-SNR in the example voxel is not too small, while the signal looks much smaller is because we happen to have low amplitudes in our design matrix. The true SNR depends on both the amplitudes in design matrix and the pseudo-SNR. Therefore, be aware that pseudo-SNR does not directly reflects how much signal the data have, but rather a map indicating the relative strength of signal in differerent voxels.\n", + "#### When you have multiple runs, the noise won't be correlated between runs. Therefore, you should tell BRSA when is the onset of each scan. \n", + "#### Note that the data (variable Y above) you feed to BRSA is the concatenation of data from all runs along the time dimension, as a 2-D matrix of time x space" ] }, { @@ -358,7 +392,7 @@ }, "outputs": [], "source": [ - "scan_onsets = np.linspace(0,design.n_TR,num=n_run+1)[:-1]\n", + "scan_onsets = np.linspace(0, design.n_TR,num=n_run + 1)[: -1]\n", "print('scan onsets: {}'.format(scan_onsets))" ] }, @@ -366,7 +400,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# (2) Fit Bayesian RSA to our simulated data" + "# Fit Bayesian RSA to our simulated data" ] }, { @@ -377,20 +411,24 @@ }, "outputs": [], "source": [ - "brsa = BRSA(GP_space=True,GP_inten=True,tau_range=10)\n", - "# Initiate an instance, telling it that we want to impose Gaussian Process prior over both space and intensity.\n", - "\n", - "brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets,\n", - " coords=coords_flat, inten=inten)\n", - "# The data to fit should be given to the argument X. Design matrix goes to design. And so on.\n" + "brsa = BRSA(GP_space=True, GP_inten=True,\n", + " tau_range=10, n_nureg=10)\n", + "# Initiate an instance, telling it\n", + "# that we want to impose Gaussian Process prior\n", + "# over both space and intensity.\n", + "\n", + "brsa.fit(X=Y, design=design.design_task,\n", + " coords=coords_flat, inten=inten, scan_onsets=scan_onsets)\n", + "# The data to fit should be given to the argument X.\n", + "# Design matrix goes to design. And so on.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### We can have a look at the estimated similarity in matrix brsa.C_ \n", - "### We can also compare the ideal covariance above with the one recovered, brsa.U_" + "### We can have a look at the estimated similarity in matrix brsa.C_. \n", + "#### We can also compare the ideal covariance above with the one recovered, brsa.U_" ] }, { @@ -409,7 +447,7 @@ "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('Estimated correlation structure\\n shared between voxels\\n'\n", - " 'This constitutes the output of BRSA\\n')\n", + " 'This constitutes the output of Bayesian RSA\\n')\n", "plt.show()\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", @@ -427,8 +465,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## In contrast, we can have a look of the similarity matrix based on Pearson correlation between point estimates of betas of different conditions.\n", - "## This is what vanila RSA might give" + "### In contrast, we can have a look of the similarity matrix based on Pearson correlation between point estimates of betas of different conditions.\n", + "#### This is what vanila RSA might give" ] }, { @@ -439,10 +477,11 @@ }, "outputs": [], "source": [ - "regressor = np.insert(design.design_used,0,1,axis=1)\n", + "regressor = np.insert(design.design_task,\n", + " 0, 1, axis=1)\n", "betas_point = np.linalg.lstsq(regressor, Y)[0]\n", - "point_corr = np.corrcoef(betas_point[1:,:])\n", - "point_cov = np.cov(betas_point[1:,:])\n", + "point_corr = np.corrcoef(betas_point[1:, :])\n", + "point_cov = np.cov(betas_point[1:, :])\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(point_corr, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", @@ -490,7 +529,8 @@ "plt.show()\n", "\n", "fig = plt.figure(num=None, figsize=(5, 5), dpi=100)\n", - "plt.pcolor(np.reshape(snr / np.exp(np.mean(np.log(snr))), [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", + "plt.pcolor(np.reshape(snr / np.exp(np.mean(np.log(snr))),\n", + " [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", "plt.colorbar()\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", @@ -510,9 +550,12 @@ "RMS_RSA = np.mean((point_corr - ideal_corr)**2)**0.5\n", "print('RMS error of Bayesian RSA: {}'.format(RMS_BRSA))\n", "print('RMS error of standard RSA: {}'.format(RMS_RSA))\n", - "print('Recovered spatial smoothness length scale: {}, vs. true value: {}'.format(brsa.lGPspace_, smooth_width))\n", - "print('Recovered intensity smoothness length scale: {}, vs. true value: {}'.format(brsa.lGPinten_, inten_kernel))\n", - "print('Recovered standard deviation of GP prior: {}, vs. true value: {}'.format(brsa.bGP_, tau))" + "print('Recovered spatial smoothness length scale: '\n", + " '{}, vs. true value: {}'.format(brsa.lGPspace_, smooth_width))\n", + "print('Recovered intensity smoothness length scale: '\n", + " '{}, vs. true value: {}'.format(brsa.lGPinten_, inten_kernel))\n", + "print('Recovered standard deviation of GP prior: '\n", + " '{}, vs. true value: {}'.format(brsa.bGP_, tau))" ] }, { @@ -522,6 +565,13 @@ "#### Empirically, the smoothness turns to be over-estimated when signal is weak." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### We can also look at how other parameters are recovered." + ] + }, { "cell_type": "code", "execution_count": null, @@ -530,14 +580,68 @@ }, "outputs": [], "source": [ - "plt.scatter(brsa.sigma_, noise_level)\n", + "plt.scatter(noise_level * np.sqrt(0.1), brsa.sigma_)\n", + "plt.xlabel('true \"independent\" noise level')\n", + "plt.ylabel('recovered \"independent\" noise level')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", "plt.show()\n", - "plt.scatter(brsa.rho_, rho1)\n", + "\n", + "plt.scatter(rho1, brsa.rho_)\n", + "plt.xlabel('true AR(1) coefficients')\n", + "plt.ylabel('recovered AR(1) coefficients')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", "plt.show()\n", - "plt.scatter(brsa.nSNR_, snr)\n", + "\n", + "plt.scatter(np.log(snr) - np.mean(np.log(snr)),\n", + " np.log(brsa.nSNR_))\n", + "plt.xlabel('true normalized log SNR')\n", + "plt.ylabel('recovered log pseudo-SNR')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Even though the variation reduced in estimated pseudo-SNR (due to overestimation of smoothness of the GP prior under low SNR situation), betas recovered by the model has higher correlation with true betas than doing simple regression, shown below. Obiously there is shrinkage of the estimated betas, as a result of variance-bias tradeoff. But we think such shrinkage does preserve the patterns of betas, and therefore the result is suitable to be further used for decoding purpose." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.scatter(betas_simulated, brsa.beta_)\n", + "plt.xlabel('true betas (response amplitudes)')\n", + "plt.ylabel('recovered betas by Bayesian RSA')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", + "plt.show()\n", + "\n", + "\n", + "plt.scatter(betas_simulated, betas_point[1:, :])\n", + "plt.xlabel('true betas (response amplitudes)')\n", + "plt.ylabel('recovered betas by simple regression')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", "plt.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The singular decomposition of noise, and the comparison between the first principal component of noise and the first principal component returned by the model." + ] + }, { "cell_type": "code", "execution_count": null, @@ -545,7 +649,23 @@ "collapsed": false }, "outputs": [], - "source": [] + "source": [ + "u, s, v = np.linalg.svd(noise)\n", + "plt.plot(s)\n", + "plt.xlabel('principal component')\n", + "plt.ylabel('singular value of simulated noise')\n", + "plt.show()\n", + "\n", + "plt.pcolor(np.reshape(v[0,:], [ROI_edge, ROI_edge]))\n", + "plt.title('Weights of the first principal component in noise')\n", + "plt.show()\n", + "\n", + "\n", + "plt.pcolor(np.reshape(brsa.beta0_[0,:], [ROI_edge, ROI_edge]))\n", + "plt.title('Weights of the first recovered principal component in noise')\n", + "plt.show()\n", + "print(brsa.beta0_.shape)" + ] } ], "metadata": { diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index 903a9b3a3..9be16e5e8 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -27,7 +27,7 @@ def test_can_instantiate(): features = 3 s = brainiak.reprsimil.brsa.BRSA(n_iter=50, rank=5, GP_space=True, GP_inten=True, tol=2e-3,\ - epsilon=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) + eta=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) assert s, "Invalid BRSA instance!" def test_fit(): @@ -43,12 +43,12 @@ def test_fit(): # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,1:17],[4,1]) + design.design_task = np.tile(design.design_task[:,:-1],[4,1]) design.n_TR = design.n_TR * 4 # start simulating some data - n_V = 300 - n_C = np.size(design.design_used,axis=1) + n_V = 200 + n_C = np.size(design.design_task,axis=1) n_T = design.n_TR noise_bot = 0.5 @@ -67,10 +67,16 @@ def test_fit(): for i_t in range(1,n_T): noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level + noise = noise + np.random.rand(n_V) + # Random baseline + # ideal covariance matrix ideal_cov = np.zeros([n_C,n_C]) ideal_cov = np.eye(n_C)*0.6 - ideal_cov[5:9,5:9] = 0.6 + ideal_cov[0:4,0:4] = 0.2 + for cond in range(0,4): + ideal_cov[cond,cond] = 2 + ideal_cov[5:9,5:9] = 0.9 for cond in range(5,9): ideal_cov[cond,cond] = 1 idx = np.where(np.sum(np.abs(ideal_cov),axis=0)>0)[0] @@ -101,7 +107,7 @@ def test_fit(): snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level sqrt_v = noise_level*snr betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v - signal = np.dot(design.design_used,betas_simulated) + signal = np.dot(design.design_task,betas_simulated) # Adding noise to signal as data Y = signal + noise @@ -111,22 +117,23 @@ def test_fit(): # Test fitting with GP prior. - brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) + brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,auto_nuiance=False) # We also test that it can detect baseline regressor included in the design matrix for task conditions - wrong_design = np.insert(design.design_used, 0, 1, axis=1) + wrong_design = np.insert(design.design_task, 0, 1, axis=1) with pytest.raises(ValueError) as excinfo: brsa.fit(X=Y, design=wrong_design, scan_onsets=scan_onsets, coords=coords, inten=inten) assert 'Your design matrix appears to have included baseline time series.' in str(excinfo.value) # Now we fit with the correct design matrix. - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, + brsa.fit(X=Y, design=design.design_task, scan_onsets=scan_onsets, coords=coords, inten=inten) # Check that result is significantly correlated with the ideal covariance matrix - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + u_b = brsa.U_ + u_i = ideal_cov + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b)], + u_i[np.tril_indices_from(u_i)])[1] assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] @@ -137,14 +144,15 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" - # Test fitting with lower rank + + # Test fitting with lower rank and without GP prior rank = n_C - 1 - brsa = BRSA(rank=rank) - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, - coords=coords, inten=inten) - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + n_nureg = 1 + brsa = BRSA(rank=rank,n_nureg=n_nureg) + brsa.fit(X=Y, design=design.design_task, scan_onsets=scan_onsets) + u_b = brsa.U_ + u_i = ideal_cov + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b)],u_i[np.tril_indices_from(u_i)])[1] assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] @@ -155,34 +163,20 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" - # Test fitting without GP prior. - brsa = BRSA() - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets) - - # Check that result is significantly correlated with the ideal covariance matrix - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] - assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" - # check that the recovered SNRs makes sense - p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" - assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" - p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" - p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" assert not hasattr(brsa,'bGP_') and not hasattr(brsa,'lGPspace_') and not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of GP if GP is not requested.' # GP parameters are not set if not requested + assert brsa.beta0_.shape[0] == n_nureg, 'Shape of beta0 incorrect' + p = scipy.stats.pearsonr(brsa.beta0_[0,:],np.mean(noise,axis=0))[1] + assert p < 0.05, 'recovered beta0 does not correlate with the baseline of voxels.' # Test fitting with GP over just spatial coordinates. brsa = BRSA(GP_space=True) - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, coords=coords) + brsa.fit(X=Y, design=design.design_task, scan_onsets=scan_onsets, coords=coords) # Check that result is significantly correlated with the ideal covariance matrix - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + u_b = brsa.U_ + u_i = ideal_cov + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b)],u_i[np.tril_indices_from(u_i)])[1] assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] @@ -211,12 +205,12 @@ def test_gradient(): design = utils.ReadDesign(fname=file_path) n_run = 4 # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,1:17],[n_run,1]) + design.design_task = np.tile(design.design_task[:,:-1],[n_run,1]) design.n_TR = design.n_TR * n_run # start simulating some data n_V = 200 - n_C = np.size(design.design_used,axis=1) + n_C = np.size(design.design_task,axis=1) n_T = design.n_TR noise_bot = 0.5 @@ -270,7 +264,7 @@ def test_gradient(): snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level sqrt_v = noise_level*snr betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v - signal = np.dot(design.design_used,betas_simulated) + signal = np.dot(design.design_task,betas_simulated) # Adding noise to signal as data Y = signal + noise @@ -286,7 +280,7 @@ def test_gradient(): XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ X0TY, X0TDY, X0TFY, X0, n_run_returned, n_base =\ - brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) + brsa._prepare_data(design.design_task,Y,n_T,scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ 'Dimension of XTY etc. returned from _prepare_data is wrong' @@ -344,17 +338,6 @@ def test_gradient(): param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' - # We test the gradient to log(sigma^2) - # vec = np.zeros(np.size(param0_sing)) - # vec[idx_param_sing['log_sigma2']] = 1 - # dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - # XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, - # XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - # l_idx, n_C, n_T, n_V, n_run, n_base, - # idx_param_sing)[0], - # param0_sing, vec) - # assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' - # We test the gradient to a1 vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['a1']] = 1 @@ -405,7 +388,7 @@ def test_gradient(): assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU incorrect' # We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior. - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ brsa._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, @@ -414,15 +397,15 @@ def test_gradient(): XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, L_full, rho1, n_V, n_base) - assert np.ndim(XTAX) == 3, 'Dimension of XTAX is wrong by _calc_sandwidge()' - assert XTAY.shape == XTY.shape, 'Shape of XTAY is wrong by _calc_sandwidge()' - assert YTAY.shape == YTY_diag.shape, 'Shape of YTAY is wrong by _calc_sandwidge()' - assert np.ndim(X0TAX0) == 3, 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' - assert np.ndim(XTAX0) == 3, 'Dimension of XTAX0 is wrong by _calc_sandwidge()' + assert np.shape(XTAcorrX) == (n_V, n_C, n_C), 'Dimension of XTAcorrX is wrong by _calc_sandwidge()' + assert XTAcorrY.shape == XTY.shape, 'Shape of XTAcorrY is wrong by _calc_sandwidge()' + assert YTAcorrY.shape == YTY_diag.shape, 'Shape of YTAcorrY is wrong by _calc_sandwidge()' + assert np.shape(X0TAX0) == (n_V, n_base, n_base), 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' + assert np.shape(XTAX0) == (n_V, n_C, n_base), 'Dimension of XTAX0 is wrong by _calc_sandwidge()' assert X0TAY.shape == X0TY.shape, 'Shape of X0TAX0 is wrong by _calc_sandwidge()' assert np.all(np.isfinite(X0TAX0_i)), 'Inverse of X0TAX0 includes NaN or Inf' ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV[idx_param_fitV['log_SNR2']], - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -430,7 +413,7 @@ def test_gradient(): idx_param_fitV,n_C,False,False) vec = np.zeros(np.size(param0_fitV[idx_param_fitV['log_SNR2']])) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -440,7 +423,7 @@ def test_gradient(): assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' # We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -449,7 +432,7 @@ def test_gradient(): dist2,inten_diff2,100,100) vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -462,7 +445,7 @@ def test_gradient(): # We test the graident wrt spatial length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_space']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -475,7 +458,7 @@ def test_gradient(): # We test the graident wrt intensity length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_inten']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -488,7 +471,7 @@ def test_gradient(): # We test the graident on a random direction vec = np.random.randn(np.size(param0_fitV)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), diff --git a/tests/utils/test_utils.py b/tests/utils/test_utils.py index 605764a6d..238b93931 100644 --- a/tests/utils/test_utils.py +++ b/tests/utils/test_utils.py @@ -58,7 +58,18 @@ def test_ReadDesign(): import numpy as np import os.path file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") - design = ReadDesign(fname=file_path) + design = ReadDesign(fname=file_path, include_orth=False, include_pols=False) assert design, 'Failed to read design matrix' + assert design.reg_nuiance is None, \ + 'Nuiance regressor is not None when include_orth and include_pols are'\ + ' both set to False' read = ReadDesign() - assert read, 'Failed to initialize an instance of the class' \ No newline at end of file + assert read, 'Failed to initialize an instance of the class' + design = ReadDesign(fname=file_path, include_orth=True, include_pols=True) + assert np.size(design.cols_nuisance) == 10, \ + 'Mistake in counting the number of nuiance regressors' + assert np.size(design.cols_task) == 17, \ + 'Mistake in counting the number of task conditions' + assert np.shape(design.reg_nuiance)[0] == np.shape(design.design_task)[0],\ + 'The number of time points in nuiance regressor does not match'\ + ' that of task respons' \ No newline at end of file From 58176f4e542207d4ec420cda86a3dce12a18e5f7 Mon Sep 17 00:00:00 2001 From: lcnature Date: Wed, 12 Oct 2016 00:43:46 -0400 Subject: [PATCH 08/30] fixed some bugs and typos --- tests/reprsimil/test_brsa.py | 29 +++++++++++------------------ tests/utils/test_utils.py | 4 ++-- 2 files changed, 13 insertions(+), 20 deletions(-) diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index 9be16e5e8..203c51cec 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -137,12 +137,12 @@ def test_fit(): assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert p < 0.01, "Fitted SNR does not correlate with simulated SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + assert p < 0.01, "Fitted noise level does not correlate with simulated noise level!" p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simulated values!" # Test fitting with lower rank and without GP prior @@ -156,12 +156,12 @@ def test_fit(): assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert p < 0.01, "Fitted SNR does not correlate with simulated SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + assert p < 0.01, "Fitted noise level does not correlate with simulated noise level!" p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simulated values!" assert not hasattr(brsa,'bGP_') and not hasattr(brsa,'lGPspace_') and not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of GP if GP is not requested.' @@ -180,12 +180,12 @@ def test_fit(): assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert p < 0.01, "Fitted SNR does not correlate with simulated SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + assert p < 0.01, "Fitted noise level does not correlate with simulated noise level!" p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simulated values!" assert not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of lGPinten_ if only smoothness in space is requested.' # GP parameters are not set if not requested @@ -241,9 +241,6 @@ def test_gradient(): # generating signal snr_level = 5.0 # test with high SNR - # snr = np.random.rand(n_V)*(snr_top-snr_bot)+snr_bot - # Notice that accurately speaking this is not snr. the magnitude of signal depends - # not only on beta but also on x. inten = np.random.randn(n_V) * 20.0 # parameters of Gaussian process to generate pseuso SNR @@ -262,6 +259,8 @@ def test_gradient(): L = np.linalg.cholesky(K) snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level + # Notice that accurately speaking this is not snr. the magnitude of signal depends + # not only on beta but also on x. sqrt_v = noise_level*snr betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v signal = np.dot(design.design_task,betas_simulated) @@ -269,10 +268,8 @@ def test_gradient(): # Adding noise to signal as data Y = signal + noise - scan_onsets = np.linspace(0,design.n_TR,num=n_run+1) - # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,rank=n_C) @@ -296,9 +293,6 @@ def test_gradient(): 'Dimension of X0TY etc. returned from _prepare_data is wrong' X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) - # rank = n_C - 1 - # idx_rank = np.where(l_idx[1] < rank) - # l_idx = (l_idx[0][idx_rank], l_idx[1][idx_rank]) n_l = np.size(l_idx[0]) # Make sure all the fields are in the indices. @@ -315,7 +309,6 @@ def test_gradient(): param0_fitU = np.random.randn(n_l+n_V) * 0.1 param0_fitV = np.random.randn(n_V+1) * 0.1 param0_sing = np.random.randn(n_l+1) * 0.1 - # param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 param0_sing[idx_param_sing['a1']] += np.mean(np.tan(rho1 * np.pi / 2)) param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 diff --git a/tests/utils/test_utils.py b/tests/utils/test_utils.py index 238b93931..3a7ef176f 100644 --- a/tests/utils/test_utils.py +++ b/tests/utils/test_utils.py @@ -60,7 +60,7 @@ def test_ReadDesign(): file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") design = ReadDesign(fname=file_path, include_orth=False, include_pols=False) assert design, 'Failed to read design matrix' - assert design.reg_nuiance is None, \ + assert design.reg_nuisance is None, \ 'Nuiance regressor is not None when include_orth and include_pols are'\ ' both set to False' read = ReadDesign() @@ -70,6 +70,6 @@ def test_ReadDesign(): 'Mistake in counting the number of nuiance regressors' assert np.size(design.cols_task) == 17, \ 'Mistake in counting the number of task conditions' - assert np.shape(design.reg_nuiance)[0] == np.shape(design.design_task)[0],\ + assert np.shape(design.reg_nuisance)[0] == np.shape(design.design_task)[0],\ 'The number of time points in nuiance regressor does not match'\ ' that of task respons' \ No newline at end of file From bdd87bf11d73dea4f6af46d7730343a33bd47426 Mon Sep 17 00:00:00 2001 From: lcnature Date: Wed, 12 Oct 2016 16:02:00 -0400 Subject: [PATCH 09/30] Removed some redundant calculation" --- brainiak/reprsimil/brsa.py | 180 ++++++++++-------- ...tational_similarity_estimate_example.ipynb | 31 +-- tests/reprsimil/test_brsa.py | 25 ++- 3 files changed, 139 insertions(+), 97 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 23e41f8c0..448a1027f 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -78,24 +78,24 @@ class BRSA(BaseEstimator): (e.g., calculating the similarity matrix of responses to each event), you might want to start with specifying a lower rank and use metrics such as AIC or BIC to decide the optimal rank. - auto_nuiance: boolean, default: True + auto_nuisance: boolean, default: True In order to model spatial correlation between voxels that cannot be accounted for by common response captured in the design matrix, we assume that a set of time courses not related to the task conditions are shared across voxels with unknown amplitudes. One approach is for users to provide time series which they consider - as nuiance but exist in the noise (such as head motion). + as nuisance but exist in the noise (such as head motion). The other way is to take the first n_nureg principal components in the residual after one fitting of the Bayesian RSA model, and use these components as the nuisance regressor. - If this flag is turned on, the nuiance regressor provided by the + If this flag is turned on, the nuisance regressor provided by the user is used only in the first round of fitting. The PCs from residuals will be used in the next round of fitting. - Note that nuiance regressor is not required from user. If it is - not provided, DC components for each run will be used as nuiance + Note that nuisance regressor is not required from user. If it is + not provided, DC components for each run will be used as nuisance regressor in the initial fitting. n_nureg: int, default: 6 - Number of nuiance regressors to use in order to model signals + Number of nuisance regressors to use in order to model signals shared across voxels not captured by the design matrix. This parameter will not be effective in the first round of fitting. GP_space: boolean, default: False @@ -178,7 +178,7 @@ class BRSA(BaseEstimator): def __init__( self, n_iter=50, rank=None, GP_space=False, GP_inten=False, - tol=2e-3, auto_nuiance=True, n_nureg=6, verbose=False, + tol=2e-3, auto_nuisance=True, n_nureg=6, verbose=False, eta=0.0001, space_smooth_range=None, inten_smooth_range=None, tau_range=10.0, init_iter=20, optimizer='BFGS', rand_seed=0): self.n_iter = n_iter @@ -186,7 +186,7 @@ def __init__( self.GP_space = GP_space self.GP_inten = GP_inten self.tol = tol - self.auto_nuiance = auto_nuiance + self.auto_nuisance = auto_nuisance self.n_nureg = n_nureg self.verbose = verbose self.eta = eta @@ -207,7 +207,7 @@ def __init__( self.rand_seed = rand_seed return - def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, + def fit(self, X, design, nuisance=None, scan_onsets=None, coords=None, inten=None): """Compute the Bayesian RSA @@ -223,12 +223,12 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, response for task conditions. You do not need to include regressors for a DC component or motion parameters, unless with a strong reason. If you want to model DC component or head motion, - you should include them in nuiance regressors. + you should include them in nuisance regressors. If you have multiple run, the design matrix of all runs should be concatenated along the time dimension, with one column across runs for each condition. - nuiance: optional, 2-D numpy array, - shape=[time_points, nuiance_factors] + nuisance: optional, 2-D numpy array, + shape=[time_points, nuisance_factors] The responses to these regressors will be marginalized out from each voxel, which means they are considered, but won't be assumed to share the same pseudo-SNR map with with the design matrix. @@ -236,14 +236,14 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, relative contribution of design matrix to each voxel. You can provide time courses such as those for head motion to this parameter. - Note that if auto_nuiance is set to True, this input + Note that if auto_nuisance is set to True, this input will only be used in the first round of fitting. The first n_nureg principal components of residual (excluding the response - to the design matrix) will be used as the nuiance regressor + to the design matrix) will be used as the nuisance regressor for the second round of fitting. - If auto_nuiance is set to False, the nuiance regressors supplied + If auto_nuisance is set to False, the nuisance regressors supplied by the users together with DC components will be used as - nuiance time series. + nuisance time series. scan_onsets: optional, an 1-D numpy array, shape=[runs,] This specifies the indices of X which correspond to the onset of each scanning run. For example, if you have two experimental @@ -296,16 +296,18 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, assert self.rank is None or self.rank <= design.shape[1],\ 'Your design matrix has fewer columns than the rank you set' - # Check the nuiance regressors. - if nuiance is not None: - assert_all_finite(nuiance) - assert np.linalg.matrix_rank(nuiance) == nuiance.shape[1], \ - 'The nuiance regressor has rank smaller than the number of'\ + # Check the nuisance regressors. + if nuisance is not None: + assert_all_finite(nuisance) + assert nuisance.ndim == 2,\ + 'The nuisance regressor should be 2 dimension ndarray' + assert np.linalg.matrix_rank(nuisance) == nuisance.shape[1], \ + 'The nuisance regressor has rank smaller than the number of'\ 'columns. Some columns can be explained by linear '\ - 'combination of other columns. Please check your nuiance' \ + 'combination of other columns. Please check your nuisance' \ 'regressors.' - assert np.size(nuiance, axis=0) == np.size(X, axis=0), \ - 'Nuiance regressor and data do not have the same '\ + assert np.size(nuisance, axis=0) == np.size(X, axis=0), \ + 'Nuisance regressor and data do not have the same '\ ' number of time points.' # check scan_onsets validity assert scan_onsets is None or\ @@ -348,7 +350,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, # without imposing any Gaussian Process prior on log(SNR^2) self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ self.sigma_, self.rho_ = \ - self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + self._fit_RSA_UV(X=design, Y=X, X0=nuisance, scan_onsets=scan_onsets) elif not self.GP_inten: # If GP_space is requested, but GP_inten is not, a GP prior @@ -356,7 +358,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ self.sigma_, self.rho_, self.lGPspace_, self.bGP_ \ = self._fit_RSA_UV( - X=design, Y=X, X0=nuiance, + X=design, Y=X, X0=nuisance, scan_onsets=scan_onsets, coords=coords) else: # If both self.GP_space and self.GP_inten are True, @@ -364,7 +366,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ self.sigma_, self.rho_, self.lGPspace_, self.bGP_,\ self.lGPinten_ = \ - self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + self._fit_RSA_UV(X=design, Y=X, X0=nuisance, scan_onsets=scan_onsets, coords=coords, inten=inten) @@ -387,7 +389,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, # For example, in X'AX = X'(I + rho1*D + rho1**2*F)X / sigma2, # the products X'X, X'DX, X'FX, etc. can always be re-used if they # are pre-calculated. Therefore, _D_gen and _F_gen constructs matrices - # D and F, and _prepare_data calculates these products that can be + # D and F, and _prepare_data_* calculates these products that can be # re-used. In principle, once parameters have been fitted for a # dataset, they can be updated for new incoming data by adding the # products X'X, X'DX, X'FX, X'Y etc. from new data to those from @@ -409,16 +411,12 @@ def _F_gen(self, TR): else: return np.empty([0, 0]) - def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): - """Prepares different forms of products of design matrix X and data Y, - or between themselves. These products are reused a lot during fitting. - So we pre-calculate them. Because of the fact that these are reused, - it is in principle possible to update the fitting as new data come in, - by just incrementally adding the products of new data and - their corresponding part of design matrix - no_DC means not inserting regressors for DC components into nuiance - regressor. It will only take effect if X0 is not None. - """ + def _prepare_DF(self, n_T, scan_onsets=None): + """ Prepare the essential template matrices D and F for + pre-calculating some terms to be re-used. + The inverse covariance matrix of AR(1) noise is + sigma^-2 * (I - rho1*D + rho1**2 * F). + And we denote A = I - rho1*D + rho1**2 * F""" if scan_onsets is None: # assume that all data are acquired within the same scan. D = np.diag(np.ones(n_T - 1), -1) + np.diag(np.ones(n_T - 1), 1) @@ -450,7 +448,18 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): F = scipy.linalg.block_diag(F, f_ele) # D and F above are templates for constructing # the inverse of temporal covariance matrix of noise - + return D, F, run_TRs, n_run + + def _prepare_data_XY(self, X, Y, D, F): + """Prepares different forms of products of design matrix X + and data Y, or between themselves. + These products are re-used a lot during fitting. + So we pre-calculate them. Because these are reused, + it is in principle possible to update the fitting + as new data come in, by just incrementally adding + the products of new data and their corresponding parts + of design matrix to these pre-calculated terms. + """ XTY, XTDY, XTFY = self._make_templates(D, F, X, Y) YTY_diag = np.sum(Y * Y, axis=0) @@ -459,6 +468,19 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): XTX, XTDX, XTFX = self._make_templates(D, F, X, X) + return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX + + def _prepare_data_XYX0(self, X, Y, X0, D, F, run_TRs, no_DC=False): + """Prepares different forms of products between design matrix X or + data Y or nuisance regressors X0 and X0. + These products are re-used a lot during fitting. + So we pre-calculate them. + no_DC means not inserting regressors for DC components + into nuisance regressor. + It will only take effect if X0 is not None. + """ + X_base = [] for r_l in run_TRs: X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)[:, None]) @@ -494,9 +516,8 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): XTX0, XTDX0, XTFX0 = self._make_templates(D, F, X, X0) X0TY, X0TDY, X0TFY = self._make_templates(D, F, X0, Y) - return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base + return X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): return XTX - rho1 * XTDX + rho1**2 * XTFX @@ -700,15 +721,18 @@ def _fit_RSA_UV(self, X, Y, X0, n_l = np.size(l_idx[0]) # the number of parameters for L + D, F, run_TRs, n_run = self._prepare_DF( + n_T, scan_onsets=scan_onsets) XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - X0=X0, no_DC=False) + XTDX, XTFX = self._prepare_data_XY(X, Y, D, F) + + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=False) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and # gradient. - # DC component will be added to the nuiance regressors. + # DC component will be added to the nuisance regressors. # In later steps, we do not need to add DC components again dist2, inten_diff2, space_smooth_range, inten_smooth_range,\ @@ -760,11 +784,10 @@ def _fit_RSA_UV(self, X, Y, X0, # Step 2 fitting, which only happens if # GP prior is requested if GP_space: - current_vec_U_chlsk_l, current_a1, current_logSNR2 \ + current_vec_U_chlsk_l, current_a1, current_logSNR2, X0 \ = self._fit_diagV_noGP( XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, @@ -794,14 +817,15 @@ def _fit_RSA_UV(self, X, Y, X0, # which might render 5 percential to 0. # Step 3 fitting. GP prior is imposed if requested. - # In this step, unless auto_nuiance is set to False, X0 + # In this step, unless auto_nuisance is set to False, X0 # will be re-estimated from the residuals after each step # of fitting. logger.debug('indexing:{}'.format(idx_param_fitV)) logger.debug('initial GP parameters:{}'.format(current_GP)) current_vec_U_chlsk_l, current_a1, current_logSNR2,\ current_GP, X0 = self._fit_diagV_GP( - X, Y, scan_onsets, X0, + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, @@ -819,11 +843,9 @@ def _fit_RSA_UV(self, X, Y, X0, # Calculating est_sigma_AR1_UV, est_sigma_AR1_UV, # est_beta_AR1_UV and est_beta0_AR1_UV - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - X0=X0, no_DC=True) + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=True) X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL\ @@ -958,8 +980,7 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, def _fit_diagV_noGP( self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, @@ -987,12 +1008,10 @@ def _fit_diagV_noGP( L = np.zeros((n_C, rank)) tol = self.tol * 5 for it in range(0, init_iter): + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=True) # fit V, reflected in the log(SNR^2) of each voxel - # XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - # XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - # X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - # = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - # X0=X0) rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ @@ -1026,7 +1045,7 @@ def _fit_diagV_noGP( '{}'.format(norm_fitVchange)) logger.debug('E[log(SNR2)^2]:'.format(np.mean(current_logSNR2**2))) - # The below lines are for debugging purpose. + # The lines below are for debugging purpose. # If any voxel's log(SNR^2) gets to non-finite number, # something might be wrong -- could be that the data has # nothing to do with the design matrix. @@ -1060,14 +1079,28 @@ def _fit_diagV_noGP( '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() + # Re-estimating X0 from residuals + current_SNR2 = np.exp(current_logSNR2) + if self.auto_nuisance: + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, current_sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, current_SNR2, + n_V, n_T, n_run, rank, n_base) + betas = current_sigma2**0.5 * current_SNR2 \ + * np.dot(L, YTAcorrXL_LAMBDA.T) + residuals = Y - np.dot(X, betas) + u, s, v = np.linalg.svd(residuals) + X0 = u[:, :self.n_nureg] + if norm_fitVchange / np.sqrt(param0_fitV.size) < tol \ and norm_fitUchange / np.sqrt(param0_fitU.size) \ < tol: break - return current_vec_U_chlsk_l, current_a1, current_logSNR2 + return current_vec_U_chlsk_l, current_a1, current_logSNR2, X0 def _fit_diagV_GP( - self, X, Y, scan_onsets, X0, + self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, l_idx, @@ -1099,11 +1132,9 @@ def _fit_diagV_GP( param0_fitV[idx_param_fitV['c_both']] = current_GP.copy() for it in range(0, n_iter): - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - X0=X0, no_DC=True) + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=True) # fit V rho1 = np.arctan(current_a1) * 2 / np.pi X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ @@ -1172,10 +1203,9 @@ def _fit_diagV_GP( '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() - current_SNR2 = np.exp(current_logSNR2) - # Re-estimating X0 from residuals - if self.auto_nuiance: + current_SNR2 = np.exp(current_logSNR2) + if self.auto_nuisance: LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, current_sigma2 \ = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, current_SNR2, diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index e78329a4f..d0d97cb9d 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -162,7 +162,9 @@ "K_noise = noise_level[:, np.newaxis] \\\n", " * (np.exp(-dist2 / noise_smooth_width**2 / 2.0) \\\n", " + np.eye(n_V) * 0.1) * noise_level\n", - "print(np.shape(K_noise))\n", + "# We make spatially correlated noise by generating\n", + "# noise at each time point from a Gaussian Process\n", + "# defined over the coordinates.\n", "plt.pcolor(K_noise)\n", "plt.colorbar()\n", "plt.xlim([0, ROI_edge * ROI_edge])\n", @@ -176,13 +178,9 @@ "for i_t in range(1, n_T):\n", " noise[i_t, :] = noise[i_t - 1, :] * rho1 \\\n", " + np.dot(L_noise,np.random.randn(n_V))\n", - "\n", - "\n", - "# noise = np.zeros([n_T,n_V])\n", - "# noise[0,:] = np.random.randn(n_V) * noise_level / np.sqrt(1-rho1**2)\n", - "# for i_t in range(1,n_T):\n", - "# noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", - "# Here, we assume noise is independent between voxels\n", + "# For each voxel, the noise follows AR(1) process:\n", + "# fresh noise plus a dampened version of noise at\n", + "# the previous time point.\n", "noise = noise + np.random.randn(n_V)\n", "fig = plt.figure(num=None, figsize=(12, 2), dpi=150,\n", " facecolor='w', edgecolor='k')\n", @@ -313,10 +311,6 @@ "# then the smoothness has much small dependency on the intensity.\n", "\n", "\n", - "# coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", - "# coords_flat = np.reshape(coords,[3, n_V]).T\n", - "# dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", - "\n", "inten = np.random.rand(n_V) * 20.0\n", "# For simplicity, we just assume that the intensity\n", "# of all voxels are uniform distributed between 0 and 20\n", @@ -580,11 +574,13 @@ }, "outputs": [], "source": [ - "plt.scatter(noise_level * np.sqrt(0.1), brsa.sigma_)\n", + "plt.scatter(noise_level * np.sqrt(0.1/1.1), brsa.sigma_)\n", "plt.xlabel('true \"independent\" noise level')\n", "plt.ylabel('recovered \"independent\" noise level')\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", + "ax.set_xticks(np.arange(0.1,0.7,0.1))\n", + "ax.set_yticks(np.arange(0.1,0.7,0.1))\n", "plt.show()\n", "\n", "plt.scatter(rho1, brsa.rho_)\n", @@ -666,6 +662,15 @@ "plt.show()\n", "print(brsa.beta0_.shape)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index 203c51cec..cfb832434 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -117,7 +117,7 @@ def test_fit(): # Test fitting with GP prior. - brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,auto_nuiance=False) + brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,auto_nuisance=False) # We also test that it can detect baseline regressor included in the design matrix for task conditions wrong_design = np.insert(design.design_task, 0, 1, axis=1) @@ -273,13 +273,19 @@ def test_gradient(): # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,rank=n_C) - # test if the gradients are correct - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run_returned, n_base =\ - brsa._prepare_data(design.design_task,Y,n_T,scan_onsets) + # Additionally, we test the generation of re-used terms. + X0 = np.ones(n_T)[:, None] + D, F, run_TRs, n_run_returned = brsa._prepare_DF( + n_T, scan_onsets=scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' - assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ + assert np.sum(run_TRs) == n_T, 'The segmentation of the total experiment duration is wrong' + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX = brsa._prepare_data_XY(design.design_task, Y, D, F) + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = brsa._prepare_data_XYX0( + design.design_task, Y, X0, D, F, run_TRs, no_DC=False) + assert np.shape(XTY) == (n_C, n_V) and np.shape(XTDY) == (n_C, n_V) \ + and np.shape(XTFY) == (n_C, n_V),\ 'Dimension of XTY etc. returned from _prepare_data is wrong' assert np.ndim(YTY_diag) == 1 and np.ndim(YTDY_diag) == 1 and np.ndim(YTFY_diag) == 1,\ 'Dimension of YTY_diag etc. returned from _prepare_data is wrong' @@ -291,10 +297,10 @@ def test_gradient(): 'Dimension of XTX0 etc. returned from _prepare_data is wrong' assert np.ndim(X0TY) == 2 and np.ndim(X0TDY) == 2 and np.ndim(X0TFY) == 2,\ 'Dimension of X0TY etc. returned from _prepare_data is wrong' - X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) n_l = np.size(l_idx[0]) + # Make sure all the fields are in the indices. idx_param_sing, idx_param_fitU, idx_param_fitV = brsa._build_index_param(n_l, n_V, 2) assert 'Cholesky' in idx_param_sing and 'a1' in idx_param_sing, \ @@ -313,7 +319,8 @@ def test_gradient(): param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 param0_fitV[idx_param_fitV['c_inten']] += np.log(inten_kernel)*2 - + + # test if the gradients are correct # log likelihood and derivative of the _singpara function ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, From 5c17970ccfd79004168b134eef7c202e1ccde671 Mon Sep 17 00:00:00 2001 From: lcnature Date: Fri, 30 Sep 2016 09:06:41 -0400 Subject: [PATCH 10/30] changed some of the logging levels --- brainiak/reprsimil/brsa.py | 59 +++++++++++++++++++------------------- 1 file changed, 30 insertions(+), 29 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index c45b074b5..2de87d265 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -233,7 +233,7 @@ def fit(self, X, design, scan_onsets=None, coords=None, some visual datasets. """ - logger.debug('Running Bayesian RSA') + logger.info('Running Bayesian RSA') assert not self.GP_inten or (self.GP_inten and self.GP_space),\ 'You must speficiy GP_space to True'\ @@ -259,8 +259,8 @@ def fit(self, X, design, scan_onsets=None, coords=None, 'Design matrix and data do not '\ 'have the same number of time points.' if self.pad_DC: - logger.debug('Padding one more column of 1 to ' - 'the end of design matrix.') + logger.info('Padding one more column of 1 to ' + 'the end of design matrix.') design = np.concatenate((design, np.ones([design.shape[0], 1])), axis=1) assert self.rank is None or self.rank <= design.shape[1],\ @@ -273,7 +273,7 @@ def fit(self, X, design, scan_onsets=None, coords=None, # check the size of coords and inten if self.GP_space: - logger.debug('Fitting with Gaussian Process prior on log(SNR)') + logger.info('Fitting with Gaussian Process prior on log(SNR)') assert coords is not None and coords.shape[0] == X.shape[1],\ 'Spatial smoothness was requested by setting GP_space. '\ 'But the voxel number of coords does not match that of '\ @@ -386,8 +386,8 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): # of 0-99 are from the first scan, 100-199 are from the second, # 200-399 are from the third and 400-499 are from the fourth run_TRs = np.diff(np.append(scan_onsets, n_T)) - logger.debug('I infer that the number of volumes' - ' in each scan are: {}'.format(run_TRs)) + logger.info('I infer that the number of volumes' + ' in each scan are: {}'.format(run_TRs)) D_ele = map(self._D_gen, run_TRs) F_ele = map(self._F_gen, run_TRs) @@ -474,7 +474,7 @@ def _build_index_param(self, n_l, n_V, n_smooth): idx_param_fitV = {'log_SNR2': np.arange(n_V - 1), 'c_space': n_V - 1, 'c_inten': n_V, 'c_both': np.arange(n_V - 1, n_V - 1 + n_smooth)} - # for the likelihood functin when we fit V (reflected by SNR of + # for the likelihood function when we fit V (reflected by SNR of # each voxel) return idx_param_sing, idx_param_fitU, idx_param_fitV @@ -506,21 +506,22 @@ def _fit_RSA_UV(self, X, Y, # The rank of covariance matrix is specified idx_rank = np.where(l_idx[1] < rank) l_idx = (l_idx[0][idx_rank], l_idx[1][idx_rank]) - logger.debug('Using the rank specified by the user: ' - '{}'.format(rank)) + logger.info('Using the rank specified by the user: ' + '{}'.format(rank)) else: rank = n_C # if not specified, we assume you want to # estimate a full rank matrix - logger.debug('Please be aware that you did not specify the rank' - ' of covariance matrix you want to estimate.' - 'I will assume that the covariance matrix shared ' - 'among voxels is of full rank.' - 'Rank = {}'.format(rank)) - logger.debug('Please be aware that estimating a matrix of ' - 'high rank can be very slow.' - 'If you have a good reason to specify a lower rank ' - 'than the number of experiment conditions, do so.') + logger.warning('Please be aware that you did not specify the' + ' rank of covariance matrix to estimate.' + 'I will assume that the covariance matrix ' + 'shared among voxels is of full rank.' + 'Rank = {}'.format(rank)) + logger.warning('Please be aware that estimating a matrix of ' + 'high rank can be very slow.' + 'If you have a good reason to specify a rank ' + 'lower than the number of experiment conditions,' + ' do so.') n_l = np.size(l_idx[0]) # the number of parameters for L @@ -665,7 +666,7 @@ def _fit_RSA_UV(self, X, Y, / n_T)**0.5 t_finish = time.time() - logger.debug( + logger.info( 'total time of fitting: {} seconds'.format(t_finish - t_start)) if GP_space: est_space_smooth_r = np.exp(current_GP[0] / 2.0) @@ -705,8 +706,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, auto-correlation). The SNR is implicitly assumed to be 1 for all voxels. """ - logger.debug('Initial fitting assuming single parameter of ' - 'noise for all voxels') + logger.info('Initial fitting assuming single parameter of ' + 'noise for all voxels') beta_hat = np.linalg.lstsq(X, Y)[0] residual = Y - np.dot(X, beta_hat) # point estimates of betas and fitting residuals without assuming @@ -778,8 +779,8 @@ def _fit_diagV_noGP( requested. """ init_iter = self.init_iter - logger.debug('second fitting without GP prior' - ' for {} times'.format(init_iter)) + logger.info('second fitting without GP prior' + ' for {} times'.format(init_iter)) # Initial parameters param0_fitU = np.empty( @@ -820,10 +821,10 @@ def _fit_diagV_noGP( # something might be wrong -- could be that the data has # nothing to do with the design matrix. if np.any(np.logical_not(np.isfinite(current_logSNR2))): - logger.debug('Initial fitting: iteration {}'.format(it)) - logger.debug('current log(SNR^2): ' - '{}'.format(current_logSNR2)) - logger.debug('log(sigma^2) has non-finite number') + logger.warning('Initial fitting: iteration {}'.format(it)) + logger.warning('current log(SNR^2): ' + '{}'.format(current_logSNR2)) + logger.warning('log(sigma^2) has non-finite number') param0_fitV = res_fitV.x.copy() @@ -865,8 +866,8 @@ def _fit_diagV_GP( """ tol = self.tol n_iter = self.n_iter - logger.debug('Last step of fitting.' - ' for maximum {} times'.format(n_iter)) + logger.info('Last step of fitting.' + ' for maximum {} times'.format(n_iter)) # Initial parameters param0_fitU = np.empty( From 0cdf658d2f652a3cd748c91526423a2b88ea48c9 Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 2 Oct 2016 23:02:12 -0400 Subject: [PATCH 11/30] Creating new functions to prepare to a new version which explicitly deals with shared time series not explained by design matrix --- brainiak/reprsimil/brsa.py | 301 ++++++++++++------ ...tational_similarity_estimate_example.ipynb | 247 +++++++++++--- tests/reprsimil/test_brsa.py | 156 +++++++-- 3 files changed, 537 insertions(+), 167 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 2de87d265..7d5f5f555 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -365,7 +365,7 @@ def _F_gen(self, TR): else: return np.empty([0, 0]) - def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): + def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): """Prepares different forms of products of design matrix X and data Y, or between themselves. These products are reused a lot during fitting. So we pre-calculate them. Because of the fact that these are reused, @@ -379,6 +379,7 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): F = np.eye(n_T) F[0, 0] = 0 F[n_T - 1, n_T - 1] = 0 + n_run = 1 else: # Each value in the scan_onsets tells the index at which # a new scan starts. For example, if n_T = 500, and @@ -386,6 +387,9 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): # of 0-99 are from the first scan, 100-199 are from the second, # 200-399 are from the third and 400-499 are from the fourth run_TRs = np.diff(np.append(scan_onsets, n_T)) + run_TRs = np.delete(run_TRs, np.where(run_TRs == 0)) + n_run = run_TRs.size + # delete run length of 0 in case of duplication in scan_onsets. logger.info('I infer that the number of volumes' ' in each scan are: {}'.format(run_TRs)) @@ -400,22 +404,85 @@ def _prepare_data(self, X, Y, n_T, n_V, scan_onsets=None): # D and F above are templates for constructing # the inverse of temporal covariance matrix of noise + XTY, XTDY, XTFY = self._make_templates(D, F, X, Y) + + YTY_diag = np.sum(Y * Y, axis=0) + YTDY_diag = np.sum(Y * np.dot(D, Y), axis=0) + YTFY_diag = np.sum(Y * np.dot(F, Y), axis=0) + + XTX, XTDX, XTFX = self._make_templates(D, F, X, X) + + X_base = [] + for r_l in run_TRs: + X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)) + res = np.linalg.lstsq(X_base.T, X) + if np.any(np.isclose(res[1], 0)): + raise ValueError('Your design matrix appears to have ' + 'included baseline time series.' + 'Either remove them, or indicates which' + ' columns in your design matrix are for ' + ' conditions of interest.') + if X0 is not None: + res0 = np.linalg.lstsq(X_base.T, X0) + if not np.any(np.isclose(res0[1], 0)): + # No columns in X0 can be explained by the + # baseline regressors. So we insert them. + X0 = np.insert(X0, 0, X_base.T, axis=1) + else: + logger.warning('Provided regressors for non-interesting ' + 'time series already include baseline. ' + 'No additional baseline is inserted.') + else: + # If a set of regressors for non-interested signals is not + # provided, then we simply include one baseline for each run. + X0 = X_base.T + logger.info('You did not provide time seres of no interest ' + 'such as DC component. One trivial regressor of' + ' DC component is included for further modeling.' + ' The final covariance matrix won''t ' + 'reflet them.') + X0TX0, X0TDX0, X0TFX0 = self._make_templates(D, F, X0, X0) + XTX0, XTDX0, XTFX0 = self._make_templates(D, F, X, X0) + X0TY, X0TDY, X0TFY = self._make_templates(D, F, X0, Y) + + return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, n_run + + def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): + return XTX - rho1 * XTDX + rho1**2 * XTFX + + def _make_sandwidge_grad(self, XTX, XTDX, XTFX, rho1): + return - XTDX + 2 * rho1 * XTFX + + def _make_templates(self, D, F, X, Y): XTY = np.dot(X.T, Y) XTDY = np.dot(np.dot(X.T, D), Y) XTFY = np.dot(np.dot(X.T, F), Y) - - YTY_diag = np.zeros([np.size(Y, axis=1)]) - YTDY_diag = np.zeros([np.size(Y, axis=1)]) - YTFY_diag = np.zeros([np.size(Y, axis=1)]) - for i_V in range(n_V): - YTY_diag[i_V] = np.dot(Y[:, i_V].T, Y[:, i_V]) - YTDY_diag[i_V] = np.dot(np.dot(Y[:, i_V].T, D), Y[:, i_V]) - YTFY_diag[i_V] = np.dot(np.dot(Y[:, i_V].T, F), Y[:, i_V]) - - XTX = np.dot(X.T, X) - XTDX = np.dot(np.dot(X.T, D), X) - XTFX = np.dot(np.dot(X.T, F), X) - return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX + return XTY, XTDY, XTFY + + def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, L, rho1): + # Calculate the sandwidge terms which put A between X, Y and X0 + # These terms are used a lot in the likelihood. But in the _fitV + # step, they only need to be calculated once, since A is fixed. + # In _fitU step, they need to be calculated at each iteration, + # because rho1 changes. + XTAY = self._make_sandwidge(XTY, XTDY, XTFY, rho1) + LTXTAY = np.dot(L.T, XTAY) + YTAY = self._make_sandwidge(YTY_diag, YTDY_diag, YTFY_diag, rho1) + XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + * XTDX[np.newaxis, :, :] \ + + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] + X0TAX0 = X0TX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + * X0TDX0[np.newaxis, :, :] \ + + rho1[:, np.newaxis, np.newaxis]**2 * X0TFX0[np.newaxis, :, :] + XTAX0 = XTX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + * XTDX0[np.newaxis, :, :] \ + + rho1[:, np.newaxis, np.newaxis]**2 * XTFX0[np.newaxis, :, :] + X0TAY = self._make_sandwidge(X0TY, X0TDY, X0TFY, rho1) + return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY def _calc_dist2_GP(self, coords=None, inten=None, GP_space=False, GP_inten=False): @@ -525,8 +592,10 @@ def _fit_RSA_UV(self, X, Y, n_l = np.size(l_idx[0]) # the number of parameters for L - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX = \ - self._prepare_data(X, Y, n_T, n_V, scan_onsets) + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, n_run \ + = self._prepare_data(X, Y, n_T, scan_onsets) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and # gradient. @@ -569,7 +638,7 @@ def _fit_RSA_UV(self, X, Y, self._initial_fit_singpara( XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, rank) current_logSNR2 = -current_logSigma2 norm_factor = np.mean(current_logSNR2) @@ -582,11 +651,13 @@ def _fit_RSA_UV(self, X, Y, if GP_space: current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 \ = self._fit_diagV_noGP( - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, rank) current_GP[0] = np.log(np.min( dist2[np.tril_indices_from(dist2, k=-1)])) @@ -616,11 +687,13 @@ def _fit_RSA_UV(self, X, Y, logger.debug('initial GP parameters:{}'.format(current_GP)) current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2,\ current_GP = self._fit_diagV_GP( - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank, + l_idx, n_C, n_T, n_V, n_l, n_run, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range) @@ -699,7 +772,7 @@ def _fit_RSA_UV(self, X, Y, def _initial_fit_singpara(self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, rank): + l_idx, n_C, n_T, n_V, n_l, n_run, rank): """ Perform initial fitting of a simplified model, which assumes that all voxels share exactly the same temporal covariance matrix for their noise (the same noise variance and @@ -756,7 +829,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, res = scipy.optimize.minimize( self._loglike_AR1_singpara, param0, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, rank), + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, options={'disp': self.verbose}) current_vec_U_chlsk_l_AR1 = res.x[idx_param_sing['Cholesky']] @@ -769,11 +843,13 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, return current_vec_U_chlsk_l_AR1, current_a1, log_sigma2 def _fit_diagV_noGP( - self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank): + l_idx, n_C, n_T, n_V, n_l, n_run, rank): """ (optional) second step of fitting, full model but without GP prior on log(SNR). This is only used when GP is requested. @@ -794,14 +870,24 @@ def _fit_diagV_noGP( param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() + L = np.zeros((n_C, rank)) tol = self.tol * 5 for it in range(0, init_iter): # fit V, reflected in the log(SNR^2) of each voxel + rho1 = np.arctan(current_a1) * 2 / np.pi + L[l_idx] = current_vec_U_chlsk_l_AR1 + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, + X0TY, X0TDY, X0TFY, L, rho1) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, - args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, - current_a1, l_idx, n_C, n_T, n_V, + args=(XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + LTXTAY, current_vec_U_chlsk_l_AR1, + current_a1, l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, rank, False, False), method=self.optimizer, jac=True, tol=tol, @@ -836,7 +922,7 @@ def _fit_diagV_noGP( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, - n_T, n_V, idx_param_fitU, rank), + n_T, n_V, n_run, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 3}) @@ -855,11 +941,13 @@ def _fit_diagV_noGP( return current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 def _fit_diagV_GP( - self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_vec_U_chlsk_l_AR1, + self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, rank, GP_space, GP_inten, + l_idx, n_C, n_T, n_V, n_l, n_run, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range): """ Last step of fitting. If GP is not requested, it will still fit. @@ -881,6 +969,7 @@ def _fit_diagV_GP( param0_fitU[idx_param_fitU['a1']] = current_a1.copy() param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() + L = np.zeros((n_C, rank)) if self.GP_space: param0_fitV[idx_param_fitV['c_both']] = current_GP.copy() # param0_fitV[idx_param_fitV['c_space']] = \ @@ -890,12 +979,20 @@ def _fit_diagV_GP( # current_GP[1] for it in range(0, n_iter): # fit V - + rho1 = np.arctan(current_a1) * 2 / np.pi + L[l_idx] = current_vec_U_chlsk_l_AR1 + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, + X0TY, X0TDY, X0TFY, L, rho1) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=( - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, - XTDY, XTFY, current_vec_U_chlsk_l_AR1, current_a1, - l_idx, n_C, n_T, n_V, idx_param_fitV, rank, + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + current_vec_U_chlsk_l_AR1, current_a1, + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range), method=self.optimizer, jac=True, @@ -927,7 +1024,7 @@ def _fit_diagV_GP( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, n_T, n_V, - idx_param_fitU, rank), + n_run, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, @@ -963,7 +1060,7 @@ def _fit_diagV_GP( def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - log_SNR2, l_idx, n_C, n_T, n_V, + log_SNR2, l_idx, n_C, n_T, n_V, n_run, idx_param_fitU, rank): # This function calculates the log likelihood of data given cholesky # decomposition of U and AR(1) parameters of noise as free parameters. @@ -995,8 +1092,6 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # Such parametrization avoids the need of boundaries # for parameters. - LL = 0.0 # log likelihood - # n_l = np.size(l_idx[0]) # the number of parameters in the index of lower-triangular matrix # This indexing allows for parametrizing only @@ -1012,10 +1107,6 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # each element of SNR2 is the ratio of the diagonal element on V # to the variance of the fresh noise in that voxel - # derivatives - deriv_L = np.zeros(np.shape(L)) - deriv_a1 = np.zeros(np.shape(rho1)) - YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag # dimension: space, # A/sigma2 is the inverse of noise covariance matrix in each voxel. @@ -1028,10 +1119,16 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # dimension: feature*space LTXTAY = np.dot(L.T, XTAY) # dimension: rank*space - LAMBDA_i = np.zeros([n_V, rank, rank]) - for i_v in range(n_V): - LAMBDA_i[i_v, :, :] = np.eye(rank) \ - + np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) * SNR2[i_v] + # LAMBDA_i = np.zeros([n_V, rank, rank]) + # for i_v in range(n_V): + # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L)\ + # * SNR2[i_v] + # LAMBDA_i += np.eye(rank) + # LTXTAXL = np.empty([n_V, rank, rank]) + # for i_v in range(n_V): + # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) + LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) + LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank LAMBDA = np.linalg.inv(LAMBDA_i) # dimension: space*rank*rank @@ -1045,35 +1142,42 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) # dimension: space*feature (feature can be larger than rank) - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) \ + # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) \ + # / n_T + sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ / n_T # dimension: space, LL = -np.sum(np.log(sigma2)) * n_T * 0.5 \ - + np.sum(np.log(1 - rho1**2)) * 0.5 \ + + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ - n_T / 2.0 + # log likelihood XTAXL = np.dot(XTAX, L) # dimension: space*feature*rank - deriv_L = -np.einsum('ijk,ikl,i', XTAXL, LAMBDA, SNR2) - \ - np.einsum('ijk,ik,il,i', XTAXL, YTAXL_LAMBDA, YTAXL_LAMBDA, - SNR2**2 / sigma2) \ + deriv_L = -np.einsum('ijk,ikl,i', XTAXL, LAMBDA, SNR2) \ + - np.dot(np.einsum('ijk,ik->ji', XTAXL, YTAXL_LAMBDA) * SNR2**2 + / sigma2, YTAXL_LAMBDA) \ + np.dot(XTAY / sigma2 * SNR2, YTAXL_LAMBDA) + # - np.einsum('ijk,ik,il,i', XTAXL, YTAXL_LAMBDA, YTAXL_LAMBDA, + # SNR2**2 / sigma2) \ # dimension: feature*rank dXTAX_drho1 = -XTDX + 2 * rho1[:, np.newaxis, np.newaxis] * XTFX # dimension: space*feature*feature - # because this term will be used twice below, we explicitly name - # it here. + dXTAY_drho1 = -XTDY + 2 * rho1 * XTFY + # dimension: feature*space + dYTAY_drho1 = -YTDY_diag + 2 * rho1 * YTFY_diag + # dimension: space, deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) * \ - (-rho1 / (1 - rho1**2) - + (-n_run * rho1 / (1 - rho1**2) - np.einsum('...ij,...ji', np.dot(LAMBDA, L.T), np.dot(dXTAX_drho1, L)) * SNR2 / 2.0 - + np.sum((-XTDY + 2.0 * rho1 * XTFY) - * YTAXL_LAMBDA_LT.T, axis=0) / sigma2 * SNR2 + + np.sum(dXTAY_drho1 * YTAXL_LAMBDA_LT.T, axis=0) + / sigma2 * SNR2 - np.einsum('...i,...ij,...j', YTAXL_LAMBDA_LT, dXTAX_drho1, YTAXL_LAMBDA_LT) / sigma2 / 2.0 * (SNR2**2.0) - - (-YTDY_diag + 2.0 * rho1 * YTFY_diag) / (sigma2 * 2.0)) + - dYTAY_drho1 / (sigma2 * 2.0)) # dimension: space, deriv = np.zeros(np.size(param)) @@ -1082,10 +1186,11 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, return -LL, -deriv - def _loglike_AR1_diagV_fitV(self, param, XTX, XTDX, XTFX, YTY_diag, - YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - L_l, a1, l_idx, n_C, n_T, n_V, idx_param_fitV, - rank=None, GP_space=False, GP_inten=False, + def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, + X0TAX0, XTAX0, X0TAY, LTXTAY, + L_l, a1, l_idx, n_C, n_T, n_V, n_run, + idx_param_fitV, rank=None, + GP_space=False, GP_inten=False, dist2=None, inten_dist2=None, space_smooth_range=None, inten_smooth_range=None): @@ -1134,47 +1239,55 @@ def _loglike_AR1_diagV_fitV(self, param, XTX, XTDX, XTFX, YTY_diag, # due to the constraint. But I have not reproduced this often. SNR2 = np.exp(log_SNR2) # If requested, a GP prior is imposed on log(SNR). - deriv_log_SNR2 = np.zeros(np.shape(SNR2)) - # Partial derivative of log likelihood over log(SNR^2) - # dimension: space, rho1 = 2.0 / np.pi * np.arctan(a1) # AR(1) coefficient, dimension: space - YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag + # YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag # dimension: space, - XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ - * XTDX[np.newaxis, :, :] \ - + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] + # XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ + # * XTDX[np.newaxis, :, :] \ + # + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] # dimension: space*feature*feature - XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY + # XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY # dimension: feature*space LTXTAY = np.dot(L.T, XTAY) # dimension: rank*space - LAMBDA_i = np.zeros([n_V, rank, rank]) - for i_v in range(n_V): - LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) \ - * SNR2[i_v] - LAMBDA_i += np.eye(rank) + # LAMBDA_i = np.zeros([n_V, rank, rank]) + # for i_v in range(n_V): + # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) \ + # * SNR2[i_v] + # LAMBDA_i += np.eye(rank) + # LTXTAXL = np.empty([n_V, rank, rank]) + # for i_v in range(n_V): + # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) + LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) + LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) + # dimension: space*rank*rank LAMBDA = np.linalg.inv(LAMBDA_i) # dimension: space*rank*rank YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) # dimension: space*rank - YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) + # YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) # dimension: space*feature - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1))\ + # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1))\ + # / n_T + sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ / n_T # dimension: space LL = -np.sum(np.log(sigma2)) * n_T * 0.5\ - + np.sum(np.log(1 - rho1**2)) * 0.5\ + + np.sum(np.log(1 - rho1**2)) * n_run * 0.5\ - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 - n_T * 0.5 # Log likelihood of data given parameters, without the GP prior. deriv_log_SNR2 = (-rank + np.trace(LAMBDA, axis1=1, axis2=2)) * 0.5\ + YTAY / (sigma2 * 2.0) - n_T * 0.5 \ - - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA_LT, - XTAX, YTAXL_LAMBDA_LT)\ + - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA, + LTXTAXL, YTAXL_LAMBDA)\ / (sigma2 * 2.0) * (SNR2**2) - + # - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA_LT, + # XTAX, YTAXL_LAMBDA_LT)\ + # Partial derivative of log likelihood over log(SNR^2) + # dimension: space, if GP_space: # Imposing GP prior on log(SNR) at least over # spatial coordinates @@ -1291,14 +1404,14 @@ def _loglike_AR1_diagV_fitV(self, param, XTX, XTDX, XTFX, YTY_diag, def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - l_idx, n_C, n_T, n_V, rank=None): + l_idx, n_C, n_T, n_V, n_run, + idx_param_sing, rank=None): # In this version, we assume that beta is independent # between voxels and noise is also independent. # singpara version uses single parameter of sigma^2 and rho1 # to all voxels. This serves as the initial fitting to get # an estimate of L and sigma^2 and rho1. The SNR is inherently # assumed to be 1. - LL = 0.0 n_l = np.size(l_idx[0]) # the number of parameters in the index of lower-triangular matrix @@ -1308,16 +1421,16 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, - np.sqrt(n_C**2 * 4 + n_C * 4 + 1 - 8 * n_l)) / 2) L = np.zeros([n_C, rank]) - L[l_idx] = param[0:n_l] + L[l_idx] = param[idx_param_sing['Cholesky']] - log_sigma2 = param[n_l] + log_sigma2 = param[idx_param_sing['log_sigma2']] sigma2 = np.exp(log_sigma2) - a1 = param[n_l + 1] + a1 = param[idx_param_sing['a1']] rho1 = 2.0 / np.pi * np.arctan(a1) XTAX = XTX - rho1 * XTDX + rho1**2 * XTFX LAMBDA_i = np.eye(rank) +\ - np.dot(np.dot(np.transpose(L), XTAX), L) / sigma2 + np.dot(np.dot(L.T, XTAX), L) / sigma2 XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY LTXTAY = np.dot(L.T, XTAY) @@ -1327,7 +1440,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, LAMBDA_LTXTAY = np.linalg.solve(LAMBDA_i, LTXTAY) L_LAMBDA_LTXTAY = np.dot(L, LAMBDA_LTXTAY) - LL = LL + np.sum(LTXTAY * LAMBDA_LTXTAY) / (sigma2**2 * 2.0) \ + LL = np.sum(LTXTAY * LAMBDA_LTXTAY) / (sigma2**2 * 2.0) \ - np.sum(YTAY) / (sigma2 * 2.0) deriv_L = np.dot(XTAY, LAMBDA_LTXTAY.T) / sigma2**2 \ @@ -1340,7 +1453,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, * L_LAMBDA_LTXTAY) / (sigma2**3 * 2.0) deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) \ - * (-rho1 / (1 - rho1**2) + * (-n_run * rho1 / (1 - rho1**2) + np.sum((-XTDY + 2 * rho1 * XTFY) * L_LAMBDA_LTXTAY) / (sigma2**2) - np.sum(np.dot((-XTDX + 2 * rho1 * XTFX), L_LAMBDA_LTXTAY) @@ -1348,7 +1461,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, - np.sum(-YTDY_diag + 2 * rho1 * YTFY_diag) / (sigma2 * 2.0)) LL = LL + np.size(YTY_diag) * (-log_sigma2 * n_T * 0.5 - + np.log(1 - rho1**2) * 0.5 + + np.log(1 - rho1**2) * n_run * 0.5 - np.log(np.linalg.det(LAMBDA_i)) * 0.5) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index a53817b9d..aa96a5f06 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false }, @@ -44,7 +44,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false }, @@ -80,17 +80,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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2bTF48GCcPn0aM2bMwIEDB0o9Bu7fvx979+5FVFQUqlWrhosXL2LGjBkICQnBiRMn/tZT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\nSUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "design = utils.ReadDesign(fname=\"example_design.1D\")\n", "\n", - "\n", - "design.design_used = np.tile(design.design_used[:,0:17],[2,1])\n", - "design.n_TR = design.n_TR * 2\n", + "n_run = 2\n", + "design.design_used = np.tile(design.design_used[:,1:17],[n_run,1])\n", + "design.n_TR = design.n_TR * n_run\n", "\n", "\n", "fig = plt.figure(num=None, figsize=(12, 3), dpi=150, facecolor='w', edgecolor='k')\n", @@ -122,11 +133,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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PwohPZnR0mKvhqSLdPDD5uT6eNHd2uk+gE91x8zNge3lmJpCeHvsAt3Ah8N57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\nLFvMVdIddvZydQ9YwLSY+1G67bKXq0p3Xp7Vos6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p5u/q9vKwlG4n0q3vHKRCn0+rSndb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\n9ttv47DDDnP9bWHhPAwatBjAYsyfvxiLFy/GrFmzLErQpk00ELByaGf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I6C4tSlJ0n3km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\n008fesyyLDz99NOO/RNCMujv7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "noise_bot = 0.5\n", "noise_top = 1.5\n", @@ -177,7 +199,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -202,11 +224,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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ffr47Z/FqIWl9ijmw4bzUZLLF7/sp201aqxhJh5MWkWpK7qAraVs2LpUHaW3V3YDHIuJB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\nSqzzQuDKiPh5iXUeAvxe0ux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axHxYOOiOUENZ09br4VrZPL1gZlYiZy+YmVlbPNI1s8oraj3d4eCga2aVV+R6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\nctA1MyuRg66ZWYkcdM3MSuSga2ZWov8P+445MMAlm/MAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# ideal covariance matrix\n", "ideal_cov = np.zeros([n_C,n_C])\n", @@ -219,8 +262,8 @@ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_cov)\n", "plt.colorbar()\n", - "plt.xlim([0,17])\n", - "plt.ylim([0,17])\n", + "plt.xlim([0,16])\n", + "plt.ylim([0,16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal covariance matrix')\n", @@ -231,8 +274,8 @@ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_corr)\n", "plt.colorbar()\n", - "plt.xlim([0,17])\n", - "plt.ylim([0,17])\n", + "plt.xlim([0,16])\n", + "plt.ylim([0,16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal correlation matrix')\n", @@ -248,11 +291,42 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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AEBAQAJ7nMX78eHTs2FHnYKcsOTg4AACePn2KmjVrit57+vSp1oH1ClNPl2Zn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FvONxWB0IxUOGd33Pp9vTrYxn4/mAEH0Qc9QzcgYjU1mjQzehHjWHUdmKUKjPou7aXMhRD8aC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\n9u3bTVZW1pT3k5KSzM6dO/2fDw4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gQQYAV18NfOc7wK5d3rZH8Ad791JlcqNVy0RUivYj0YS+64V6Vxf9/7Zt9NjI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\n0TvqeXn2awyJUBe0iFCPE23oe0kJXYx6V0+b6+y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kCGnDkSIJ9WRy1K2E+u7dobm6ZkJd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AewfAv1QYPIJcxVqLuVZ+vtpZDMQnDUUyngy18G/u3fjMRydvvUc80SW1MTXjK5fDjqhw8HdzYu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\nQm9vr+v/3nnnnRg1ahRqampw4YUXoqWlJ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "\n", @@ -348,13 +422,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "scan onsets: [ 0. 186.]\n" + ] + } + ], "source": [ - "scan_onsets = np.linspace(0,design.n_TR,num=3)[:-1]\n", + "scan_onsets = np.linspace(0,design.n_TR,num=n_run+1)[:-1]\n", "print('scan onsets: {}'.format(scan_onsets))" ] }, @@ -367,11 +449,25 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "BRSA(GP_inten=True, GP_space=True, epsilon=0.0001, init_iter=20,\n", + " inten_smooth_range=None, n_iter=50, optimizer='BFGS', pad_DC=False,\n", + " rand_seed=0, rank=None, space_smooth_range=None, tau_range=10,\n", + " tol=0.002, verbose=False)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "brsa = BRSA(GP_space=True,GP_inten=True,tau_range=10)\n", "# Initiate an instance, telling it that we want to impose Gaussian Process prior over both space and intensity.\n", @@ -391,14 +487,35 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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XqH9yzFcIoTE/E+t9lDBbPddCxpgCF7M4L2I13GVmDybG/wJwDbBt4jF/Z0KM6Y7UmP5K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\ntjE0deYcc3HtS0j94jiOUx9taHNu2sx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7AFsDT7dWNeecc41oumulkcnYJb0bOA3YHbgyTwWdc877yLO1vY88BvdzgVPM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\nIHfOuQ73/wHFGIT2j2SJawAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(brsa.C_[1:, 1:], vmin=-0.1, vmax=1)\n", + "plt.pcolor(brsa.C_, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", "plt.ylim([0, 16])\n", "plt.colorbar()\n", @@ -410,8 +527,8 @@ "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(brsa.U_)\n", - "plt.xlim([0, 17])\n", - "plt.ylim([0, 17])\n", + "plt.xlim([0, 16])\n", + "plt.ylim([0, 16])\n", "plt.colorbar()\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", @@ -429,17 +546,38 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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f63/F89kT928F9MXvpifKLWU1r2SYz47H/i/CYkz7ADdH3XePx/mLeK3dT3iCeH+ifTdh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\nKT5idhyn8PjMP8dxnILRaTP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dC/tpnZ+tlf2sYllSQ3RtYBFwE7BDRHS9wdnH03yY2cDoUVdGRPyhUcqI2Lfm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\nZjOzknFgNjMrGQdmM7OScWA2MyuZ/w9Ad/Bd4e6ZhQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "betas_point = np.linalg.lstsq(design.design_used, Y)[0]\n", "point_corr = np.corrcoef(betas_point)\n", "point_cov = np.cov(betas_point) \n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(point_corr[1:, 1:], vmin=-0.1, vmax=1)\n", + "plt.pcolor(point_corr, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", "plt.ylim([0, 16])\n", "plt.colorbar()\n", @@ -450,7 +588,7 @@ "plt.show()\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(point_cov[1:, 1:])\n", + "plt.pcolor(point_cov)\n", "plt.xlim([0, 16])\n", "plt.ylim([0, 16])\n", "plt.colorbar()\n", @@ -470,11 +608,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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1u9T+4xh+vfNtrL1+9XCG/45p2AaySNpf0s8lPSlpQNK7ql7/frG98nF1bjtm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\nMDEz/tLMb8MvKvGR8Td54Rv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Z8TXq4AUMLZOMzMysHx38nVGL5kgzMxtOPDIyM2sXHTwycjIyM2sXXk1nZmY2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\n4y/7zUIXdu7XZw+7Km+Hbc/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig = plt.figure(num=None, figsize=(5, 5), dpi=100)\n", "plt.pcolor(np.reshape(brsa.nSNR_, [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", @@ -495,14 +654,26 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RMS error of Bayesian RSA: 0.13665981702261623\n", + "RMS error of standard RSA: 0.1433569522028947\n", + "Recovered spatial smoothness length scale: 5.595133988654466, vs. true value: 3.0\n", + "Recovered intensity smoothness length scale: 4.611783121422689, vs. true value: 4.0\n", + "Recovered standard deviation of GP prior: 0.184521447350508, vs. true value: 0.8\n" + ] + } + ], "source": [ - "RMS_BRSA = np.mean((brsa.C_[1:,1:] - ideal_corr[1:,1:])**2)**0.5\n", - "RMS_RSA = np.mean((point_corr[1:,1:] - ideal_corr[1:,1:])**2)**0.5\n", + "RMS_BRSA = np.mean((brsa.C_ - ideal_corr)**2)**0.5\n", + "RMS_RSA = np.mean((point_corr - ideal_corr)**2)**0.5\n", "print('RMS error of Bayesian RSA: {}'.format(RMS_BRSA))\n", "print('RMS error of standard RSA: {}'.format(RMS_RSA))\n", "print('Recovered spatial smoothness length scale: {}, vs. true value: {}'.format(brsa.lGPspace_, smooth_width))\n", diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index fad358938..a1aea8799 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -40,8 +40,10 @@ def test_fit(): file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") # Load an example design matrix design = utils.ReadDesign(fname=file_path) + + # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,0:17],[4,1]) + design.design_used = np.tile(design.design_used[:,1:17],[4,1]) design.n_TR = design.n_TR * 4 # start simulating some data @@ -112,6 +114,13 @@ def test_fit(): # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) + # We also test that it can detect baseline regressor included in the design matrix for task conditions + wrong_design = np.insert(design.design_used, 0, 1, axis=1) + with pytest.raises(ValueError) as excinfo: + brsa.fit(X=Y, design=wrong_design, scan_onsets=scan_onsets, + coords=coords, inten=inten) + assert 'Your design matrix appears to have included baseline time series.' in str(excinfo.value) + # Now we fit with the correct design matrix. brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, coords=coords, inten=inten) @@ -167,13 +176,15 @@ def test_gradient(): import numpy as np import os.path import numdifftools as nd + np.random.seed(100) file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") # Load an example design matrix design = utils.ReadDesign(fname=file_path) + n_run = 4 # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,0:17],[4,1]) - design.n_TR = design.n_TR * 4 + design.design_used = np.tile(design.design_used[:,1:17],[n_run,1]) + design.n_TR = design.n_TR * n_run # start simulating some data n_V = 200 @@ -237,36 +248,96 @@ def test_gradient(): Y = signal + noise - scan_onsets = np.linspace(0,design.n_TR,num=5) + scan_onsets = np.linspace(0,design.n_TR,num=n_run+1) # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) # test if the gradients are correct - XTY,XTDY,XTFY,YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX = brsa._prepare_data(design.design_used,Y,n_T,n_V,scan_onsets) + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, n_run_returned =\ + brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) + assert n_run_returned == n_run, 'There is mistake in counting number of runs' + assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ + 'Dimension of XTY etc. returned from _prepare_data is wrong' + assert np.ndim(YTY_diag) == 1 and np.ndim(YTDY_diag) == 1 and np.ndim(YTFY_diag) == 1,\ + 'Dimension of YTY_diag etc. returned from _prepare_data is wrong' + assert np.ndim(XTX) == 2 and np.ndim(XTDX) == 2 and np.ndim(XTFX) == 2,\ + 'Dimension of XTX etc. returned from _prepare_data is wrong' + assert np.ndim(X0TX0) == 2 and np.ndim(X0TDX0) == 2 and np.ndim(X0TFX0) == 2,\ + 'Dimension of X0TX0 etc. returned from _prepare_data is wrong' + assert np.ndim(XTX0) == 2 and np.ndim(XTDX0) == 2 and np.ndim(XTFX0) == 2,\ + 'Dimension of XTX0 etc. returned from _prepare_data is wrong' + assert np.ndim(X0TY) == 2 and np.ndim(X0TDY) == 2 and np.ndim(X0TFY) == 2,\ + 'Dimension of X0TY etc. returned from _prepare_data is wrong' l_idx = np.tril_indices(n_C) n_l = np.size(l_idx[0]) + # Make sure all the fields are in the indices. idx_param_sing, idx_param_fitU, idx_param_fitV = brsa._build_index_param(n_l, n_V, 2) - + assert 'Cholesky' in idx_param_sing and 'log_sigma2' in idx_param_sing \ + and 'a1' in idx_param_sing, 'The dictionary for parameter indexing misses some keys' + assert 'Cholesky' in idx_param_fitU and 'a1' in idx_param_fitU, \ + 'The dictionary for parameter indexing misses some keys' + assert 'log_SNR2' in idx_param_fitV and 'c_space' in idx_param_fitV \ + and 'c_inten' in idx_param_fitV and 'c_both' in idx_param_fitV, \ + 'The dictionary for parameter indexing misses some keys' + # Initial parameters are correct parameters with some perturbation param0_fitU = np.random.randn(n_l+n_V) * 0.1 param0_fitV = np.random.randn(n_V+1) * 0.1 - param0_fitV[:n_V-1] += np.log(snr[:n_V-1])*2 - param0_fitV[n_V-1] += np.log(smooth_width)*2 - param0_fitV[n_V] += np.log(inten_kernel)*2 + param0_sing = np.random.randn(n_l+2) * 0.1 + param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 + param0_sing[idx_param_sing['a1']] += np.mean(np.tan(rho1 * np.pi / 2)) + param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 + param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 + param0_fitV[idx_param_fitV['c_inten']] += np.log(inten_kernel)*2 + + # log likelihood and derivative of the _singpara function + ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing) + # We test the gradient to the Cholesky factor + vec = np.zeros(np.size(param0_sing)) + vec[idx_param_sing['Cholesky'][0]] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing)[0], + param0_sing, vec) + assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' + + # We test the gradient to log(sigma^2) + vec = np.zeros(np.size(param0_sing)) + vec[idx_param_sing['log_sigma2']] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing)[0], + param0_sing, vec) + assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' + + # We test the gradient to a1 + vec = np.zeros(np.size(param0_sing)) + vec[idx_param_sing['a1']] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + idx_param_sing)[0], + param0_sing, vec) + assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt a1 is incorrect' - # log likelihood and derivative at the initial parameters + + # log likelihood and derivative of the fitU function. ll0, deriv0 = brsa._loglike_AR1_diagV_fitU(param0_fitU, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, \ - XTY, XTDY, XTFY, np.log(snr)*2, l_idx,n_C,n_T,n_V,idx_param_fitU,n_C) + XTY, XTDY, XTFY, np.log(snr)*2, l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C) # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct vec = np.zeros(np.size(param0_fitU)) vec[idx_param_fitU['Cholesky'][0]] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec) + l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], + param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect' # We test the gradient wrt the reparametrization of AR(1) coefficient of noise. @@ -274,7 +345,8 @@ def test_gradient(): vec[idx_param_fitU['a1'][0]] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec) + l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], + param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt to AR(1) coefficient incorrect' # Test on a random direction @@ -282,32 +354,46 @@ def test_gradient(): vec = vec / np.linalg.norm(vec) dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec) + l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], + param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU incorrect' # We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior. + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + brsa._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, + X0TY, X0TDY, X0TFY, L_full, rho1) + assert np.ndim(XTAX) == 3, 'Dimension of XTAX is wrong by _calc_sandwidge()' + assert XTAY.shape == XTY.shape, 'Shape of XTAY is wrong by _calc_sandwidge()' + assert YTAY.shape == YTY_diag.shape, 'Shape of YTAY is wrong by _calc_sandwidge()' + assert np.ndim(X0TAX0) == 3, 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' + assert np.ndim(XTAX0) == 3, 'Dimension of XTAX0 is wrong by _calc_sandwidge()' + assert X0TAY.shape == X0TY.shape, 'Shape of X0TAX0 is wrong by _calc_sandwidge()' ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV[idx_param_fitV['log_SNR2']], - XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,idx_param_fitV,n_C,False,False) + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,False,False) vec = np.zeros(np.size(param0_fitV[idx_param_fitV['log_SNR2']])) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, False, False)[0], + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, False, False)[0], param0_fitV[idx_param_fitV['log_SNR2']], vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' # We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,idx_param_fitV,n_C,True,True, + ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,True,True, dist2,inten_diff2,100,100) vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV srt log(SNR2) incorrect for model with GP' @@ -315,9 +401,9 @@ def test_gradient(): # We test the graident wrt spatial length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_space']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt spatial length scale of GP incorrect' @@ -325,9 +411,9 @@ def test_gradient(): # We test the graident wrt intensity length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_inten']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt intensity length scale of GP incorrect' @@ -335,9 +421,9 @@ def test_gradient(): # We test the graident on a random direction vec = np.random.randn(np.size(param0_fitV)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, idx_param_fitV, n_C, True, True, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + L_full[l_idx], np.tan(rho1*np.pi/2), + l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV incorrect' From 0ec6a09fcb7c983ae3a5cb0779128b7d273d552d Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 2 Oct 2016 23:16:34 -0400 Subject: [PATCH 12/30] Further changing singpara, preparing to deal with shared time series X0 --- brainiak/reprsimil/brsa.py | 23 ++++++++++++++++------- tests/reprsimil/test_brsa.py | 19 ++++++++++++++----- 2 files changed, 30 insertions(+), 12 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 7d5f5f555..62e385045 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -447,7 +447,7 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, n_run + X0TY, X0TDY, X0TFY, X0, n_run def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): return XTX - rho1 * XTDX + rho1**2 * XTFX @@ -594,7 +594,7 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, n_run \ + X0TY, X0TDY, X0TFY, X0, n_run \ = self._prepare_data(X, Y, n_T, scan_onsets) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and @@ -637,7 +637,9 @@ def _fit_RSA_UV(self, X, Y, current_vec_U_chlsk_l_AR1, current_a1, current_logSigma2 = \ self._initial_fit_singpara( XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X, Y, idx_param_sing, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + X, X0, Y, idx_param_sing, l_idx, n_C, n_T, n_V, n_l, n_run, rank) current_logSNR2 = -current_logSigma2 @@ -771,7 +773,9 @@ def _fit_RSA_UV(self, X, Y, def _initial_fit_singpara(self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X, Y, idx_param_sing, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + X, X0, Y, idx_param_sing, l_idx, n_C, n_T, n_V, n_l, n_run, rank): """ Perform initial fitting of a simplified model, which assumes that all voxels share exactly the same temporal covariance @@ -781,8 +785,9 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, """ logger.info('Initial fitting assuming single parameter of ' 'noise for all voxels') - beta_hat = np.linalg.lstsq(X, Y)[0] - residual = Y - np.dot(X, beta_hat) + X_joint = np.concatenate((X0, X), axis=1) + beta_hat = np.linalg.lstsq(X_joint, Y)[0] + residual = Y - np.dot(X_joint, beta_hat) # point estimates of betas and fitting residuals without assuming # the Bayesian model underlying RSA. @@ -829,7 +834,9 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, res = scipy.optimize.minimize( self._loglike_AR1_singpara, param0, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, options={'disp': self.verbose}) @@ -1404,6 +1411,8 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, l_idx, n_C, n_T, n_V, n_run, idx_param_sing, rank=None): # In this version, we assume that beta is independent diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index a1aea8799..e487db9b0 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -257,7 +257,7 @@ def test_gradient(): # test if the gradients are correct XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, n_run_returned =\ + X0TY, X0TDY, X0TFY, X0, n_run_returned =\ brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ @@ -272,6 +272,7 @@ def test_gradient(): 'Dimension of XTX0 etc. returned from _prepare_data is wrong' assert np.ndim(X0TY) == 2 and np.ndim(X0TDY) == 2 and np.ndim(X0TFY) == 2,\ 'Dimension of X0TY etc. returned from _prepare_data is wrong' + X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) n_l = np.size(l_idx[0]) @@ -297,13 +298,17 @@ def test_gradient(): # log likelihood and derivative of the _singpara function ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing) # We test the gradient to the Cholesky factor vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['Cholesky'][0]] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' @@ -312,7 +317,9 @@ def test_gradient(): vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['log_sigma2']] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' @@ -321,7 +328,9 @@ def test_gradient(): vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['a1']] = 1 dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, l_idx, n_C, n_T, n_V, n_run, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + l_idx, n_C, n_T, n_V, n_run, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt a1 is incorrect' From a5cd4ac3ad8e3c231782d3e388b491d34e794180 Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 6 Oct 2016 14:06:55 -0400 Subject: [PATCH 13/30] Changed the model to consider spatial correlation in noise --- brainiak/reprsimil/brsa.py | 530 ++++++++++-------- ...tational_similarity_estimate_example.ipynb | 271 +++------ tests/reprsimil/test_brsa.py | 173 ++++-- 3 files changed, 476 insertions(+), 498 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 62e385045..39b2559c1 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -92,15 +92,6 @@ class BRSA(BaseEstimator): tol: tolerance parameter passed to the minimizer. verbose : boolean, default: False Verbose mode flag. - pad_DC: boolean, default: False - A column of all 1's will be padded to end of the design matrix - to account for residual baseline component in the signal. - We recommend removing DC component in your data but still - set this as True. If you include a baseline column yourself, - then you should check this as False. - In future version, we will include a seperate input - argument for all regressors you are not interested in, - such as DC component and motion parameters. epsilon: a small number added to the diagonal element of the covariance matrix in the Gaussian Process prior. This is to ensure that the matrix is invertible. @@ -121,7 +112,7 @@ class BRSA(BaseEstimator): tau_range: the reasonable range of the standard deviation of the Gaussian Process. Since the Gaussian Process is imposed on the log(SNR), this range should not be too - large. 5 is a pretty loose range. This parameter is + large. 10 is a pretty loose range. This parameter is used in a half-Cauchy prior on the standard deviation init_iter: how many initial iterations to fit the model without introducing the GP prior before fitting with it, @@ -167,16 +158,15 @@ class BRSA(BaseEstimator): def __init__( self, n_iter=50, rank=None, GP_space=False, GP_inten=False, - tol=2e-3, verbose=False, pad_DC=False, epsilon=0.0001, + tol=2e-3, verbose=False, epsilon=0.0001, space_smooth_range=None, inten_smooth_range=None, - tau_range=5.0, init_iter=20, optimizer='BFGS', rand_seed=0): + tau_range=10.0, init_iter=20, optimizer='BFGS', rand_seed=0): self.n_iter = n_iter self.rank = rank self.GP_space = GP_space self.GP_inten = GP_inten self.tol = tol self.verbose = verbose - self.pad_DC = pad_DC self.epsilon = epsilon # This is a tiny ridge added to the Gaussian Process # covariance matrix template to gaurantee that it is invertible. @@ -207,8 +197,10 @@ def fit(self, X, design, scan_onsets=None, coords=None, the time dimension after proper preprocessing (e.g. spatial alignment), and specify the onsets of each scan in scan_onsets. design: 2-D numpy array, shape=[time_points, conditions] - This is the design matrix. We will automatically pad a column - of all one's if pad_DC is True. + This is the design matrix. It should only include the hypothetic + response for task conditions. You do not need to include + regressors for a DC component or motion parameters, unless with + a strong reason. scan_onsets: optional, an 1-D numpy array, shape=[runs,] this specifies the indices of X which correspond to the onset of each scanning run. For example, if you have two experimental @@ -251,18 +243,13 @@ def fit(self, X, design, scan_onsets=None, coords=None, assert_all_finite(design) assert design.ndim == 2,\ 'The design matrix should be 2 dimension ndarray' - assert (not np.all(np.std(design, axis=0) > 0) and self.pad_DC)\ - or not self.pad_DC, \ - 'You already included DC component in the '\ - 'design matrix. Please set pad_DC as False' + assert np.linalg.matrix_rank(design) == design.shape[1], \ + 'Your design matrix has rank smaller than the number of'\ + ' columns. Some columns can be explained by linear '\ + 'combination of other columns. Please check your design matrix.' assert np.size(design, axis=0) == np.size(X, axis=0),\ 'Design matrix and data do not '\ 'have the same number of time points.' - if self.pad_DC: - logger.info('Padding one more column of 1 to ' - 'the end of design matrix.') - design = np.concatenate((design, - np.ones([design.shape[0], 1])), axis=1) assert self.rank is None or self.rank <= design.shape[1],\ 'Your design matrix has fewer columns than the rank you set' @@ -321,9 +308,6 @@ def fit(self, X, design, scan_onsets=None, coords=None, self._fit_RSA_UV(X=design, Y=X, scan_onsets=scan_onsets, coords=coords, inten=inten) - if self.pad_DC: - self.U_ = self.U_[:-1, :-1] - self.L_ = self.L_[:-1, :self.rank] self.C_ = utils.cov2corr(self.U_) return self @@ -380,6 +364,7 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): F[0, 0] = 0 F[n_T - 1, n_T - 1] = 0 n_run = 1 + run_TRs = np.array([n_T]) else: # Each value in the scan_onsets tells the index at which # a new scan starts. For example, if n_T = 500, and @@ -414,8 +399,8 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): X_base = [] for r_l in run_TRs: - X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)) - res = np.linalg.lstsq(X_base.T, X) + X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)[:, None]) + res = np.linalg.lstsq(X_base, X) if np.any(np.isclose(res[1], 0)): raise ValueError('Your design matrix appears to have ' 'included baseline time series.' @@ -423,11 +408,11 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): ' columns in your design matrix are for ' ' conditions of interest.') if X0 is not None: - res0 = np.linalg.lstsq(X_base.T, X0) + res0 = np.linalg.lstsq(X_base, X0) if not np.any(np.isclose(res0[1], 0)): # No columns in X0 can be explained by the # baseline regressors. So we insert them. - X0 = np.insert(X0, 0, X_base.T, axis=1) + X0 = np.insert(X0, 0, X_base, axis=1) else: logger.warning('Provided regressors for non-interesting ' 'time series already include baseline. ' @@ -435,24 +420,25 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): else: # If a set of regressors for non-interested signals is not # provided, then we simply include one baseline for each run. - X0 = X_base.T + X0 = X_base logger.info('You did not provide time seres of no interest ' 'such as DC component. One trivial regressor of' ' DC component is included for further modeling.' ' The final covariance matrix won''t ' 'reflet them.') + n_base = X0.shape[1] X0TX0, X0TDX0, X0TFX0 = self._make_templates(D, F, X0, X0) XTX0, XTDX0, XTFX0 = self._make_templates(D, F, X, X0) X0TY, X0TDY, X0TFY = self._make_templates(D, F, X0, Y) return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run + X0TY, X0TDY, X0TFY, X0, n_run, n_base def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): return XTX - rho1 * XTDX + rho1**2 * XTFX - def _make_sandwidge_grad(self, XTX, XTDX, XTFX, rho1): + def _make_sandwidge_grad(self, XTDX, XTFX, rho1): return - XTDX + 2 * rho1 * XTFX def _make_templates(self, D, F, X, Y): @@ -463,26 +449,58 @@ def _make_templates(self, D, F, X, Y): def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, L, rho1): + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base): # Calculate the sandwidge terms which put A between X, Y and X0 # These terms are used a lot in the likelihood. But in the _fitV # step, they only need to be calculated once, since A is fixed. # In _fitU step, they need to be calculated at each iteration, # because rho1 changes. XTAY = self._make_sandwidge(XTY, XTDY, XTFY, rho1) - LTXTAY = np.dot(L.T, XTAY) + # dimension: feature*space YTAY = self._make_sandwidge(YTY_diag, YTDY_diag, YTFY_diag, rho1) + # dimension: space, + # A/sigma2 is the inverse of noise covariance matrix in each voxel. + # YTAY means Y'AY XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ * XTDX[np.newaxis, :, :] \ + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] + # dimension: space*feature*feature X0TAX0 = X0TX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ * X0TDX0[np.newaxis, :, :] \ + rho1[:, np.newaxis, np.newaxis]**2 * X0TFX0[np.newaxis, :, :] + # dimension: space*#baseline*#baseline XTAX0 = XTX0[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ * XTDX0[np.newaxis, :, :] \ + rho1[:, np.newaxis, np.newaxis]**2 * XTFX0[np.newaxis, :, :] + # dimension: space*feature*#baseline X0TAY = self._make_sandwidge(X0TY, X0TDY, X0TFY, rho1) - return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY + # dimension: #baseline*space + X0TAX0_i = np.linalg.solve(X0TAX0, np.identity(n_base)[None, :, :]) + # dimension: space*#baseline*#baseline + XTAcorrX = XTAX.copy() + # dimension: space*feature*feature + XTAcorrY = XTAY.copy() + # dimension: feature*space + for i_v in range(n_V): + XTAcorrX[i_v, :, :] -= \ + np.dot(np.dot(XTAX0[i_v, :, :], X0TAX0_i[i_v, :, :]), + XTAX0[i_v, :, :].T) + XTAcorrY[:, i_v] -= np.dot(np.dot(XTAX0[i_v, :, :], + X0TAX0_i[i_v, :, :]), + X0TAY[:, i_v]) + XTAcorrXL = np.dot(XTAcorrX, L) + # dimension: space*feature*rank + LTXTAcorrXL = np.tensordot(XTAcorrXL, L, axes=(1, 0)) + # dimension: rank*feature*rank + LTXTAcorrY = np.dot(L.T, XTAcorrY) + # dimension: rank*space + YTAcorrY = YTAY - np.sum(X0TAY * np.einsum('ijk,ki->ji', + X0TAX0_i, X0TAY), axis=0) + # dimension: space + + return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL def _calc_dist2_GP(self, coords=None, inten=None, GP_space=False, GP_inten=False): @@ -532,8 +550,7 @@ def _build_index_param(self, n_l, n_V, n_smooth): """ Build dictionaries to retrieve each parameter from the combined parameters. """ - idx_param_sing = {'Cholesky': np.arange(n_l), - 'log_sigma2': n_l, 'a1': n_l + 1} + idx_param_sing = {'Cholesky': np.arange(n_l), 'a1': n_l} # for simplified fitting idx_param_fitU = {'Cholesky': np.arange(n_l), 'a1': np.arange(n_l, n_l + n_V)} @@ -594,7 +611,7 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run \ + X0TY, X0TDY, X0TFY, X0, n_run, n_base \ = self._prepare_data(X, Y, n_T, scan_onsets) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and @@ -640,13 +657,13 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, X, X0, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, n_run, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank) current_logSNR2 = -current_logSigma2 norm_factor = np.mean(current_logSNR2) current_logSNR2 = current_logSNR2 - norm_factor - current_vec_U_chlsk_l_AR1 = current_vec_U_chlsk_l_AR1 \ - * np.exp(norm_factor / 2.0) + # current_vec_U_chlsk_l_AR1 = current_vec_U_chlsk_l_AR1 \ + # * np.exp(norm_factor / 2.0) # Step 2 fitting, which only happens if # GP prior is requested @@ -659,7 +676,7 @@ def _fit_RSA_UV(self, X, Y, current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank) + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank) current_GP[0] = np.log(np.min( dist2[np.tril_indices_from(dist2, k=-1)])) @@ -695,7 +712,7 @@ def _fit_RSA_UV(self, X, Y, current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank, + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range) @@ -709,36 +726,24 @@ def _fit_RSA_UV(self, X, Y, est_SNR_AR1_UV = np.exp(current_logSNR2 / 2.0) # Calculating est_sigma_AR1_UV - YTAY = YTY_diag - est_rho1_AR1_UV * YTDY_diag + \ - est_rho1_AR1_UV**2 * YTFY_diag - XTAX = XTX[np.newaxis, :, :] \ - - est_rho1_AR1_UV[:, np.newaxis, np.newaxis] \ - * XTDX[np.newaxis, :, :] \ - + est_rho1_AR1_UV[:, np.newaxis, np.newaxis]**2\ - * XTFX[np.newaxis, :, :] - # dimension: space*feature*feature - XTAY = XTY - est_rho1_AR1_UV * XTDY + est_rho1_AR1_UV**2 * XTFY - # dimension: feature*space - LTXTAY = np.dot(estU_chlsk_l_AR1_UV.T, XTAY) - # dimension: rank*space - - LAMBDA_i = np.zeros([n_V, rank, rank]) - for i_v in range(n_V): - LAMBDA_i[i_v, :, :] = np.dot(np.dot( - estU_chlsk_l_AR1_UV.T, XTAX[i_v, :, :]), estU_chlsk_l_AR1_UV)\ - * est_SNR_AR1_UV[i_v]**2 - LAMBDA_i += np.eye(rank) + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL\ + = self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + estU_chlsk_l_AR1_UV, est_rho1_AR1_UV, + n_V, n_base) + LAMBDA_i = LTXTAcorrXL * est_SNR_AR1_UV[:, None, None]**2 \ + + np.eye(rank) # dimension: space*rank*rank - LAMBDA = np.linalg.inv(LAMBDA_i) + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) # dimension: space*rank*rank - YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) + YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) # dimension: space*rank - YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, estU_chlsk_l_AR1_UV.T) - # dimension: space*feature - - est_sigma_AR1_UV = ((YTAY - est_SNR_AR1_UV**2 * - np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) - / n_T)**0.5 + est_sigma_AR1_UV = ((YTAcorrY - np.sum(LTXTAcorrY + * YTAcorrXL_LAMBDA.T, axis=0) + * est_SNR_AR1_UV**2) / (n_T - n_base)) ** 0.5 t_finish = time.time() logger.info( @@ -775,8 +780,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - X, X0, Y, idx_param_sing, - l_idx, n_C, n_T, n_V, n_l, n_run, rank): + X, X0, Y, idx_param_sing, l_idx, + n_C, n_T, n_V, n_l, n_run, n_base, rank): """ Perform initial fitting of a simplified model, which assumes that all voxels share exactly the same temporal covariance matrix for their noise (the same noise variance and @@ -828,7 +833,7 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, # Then we fill each part of the original guess of parameters param0[idx_param_sing['Cholesky']] = current_vec_U_chlsk_l_AR1 param0[idx_param_sing['a1']] = np.median(np.tan(rho1 * np.pi / 2)) - param0[idx_param_sing['log_sigma2']] = np.median(log_sigma2) + # param0[idx_param_sing['log_sigma2']] = np.median(log_sigma2) # Fit it. res = scipy.optimize.minimize( @@ -836,10 +841,10 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, - options={'disp': self.verbose}) + options={'disp': self.verbose, 'maxiter': 100}) current_vec_U_chlsk_l_AR1 = res.x[idx_param_sing['Cholesky']] current_a1 = res.x[idx_param_sing['a1']] * np.ones(n_V) # log(sigma^2) assuming the data include no signal is returned, @@ -856,7 +861,7 @@ def _fit_diagV_noGP( current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank): + l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank): """ (optional) second step of fitting, full model but without GP prior on log(SNR). This is only used when GP is requested. @@ -883,19 +888,24 @@ def _fit_diagV_noGP( # fit V, reflected in the log(SNR^2) of each voxel rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, \ + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, - X0TY, X0TDY, X0TFY, L, rho1) + X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=(XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, - LTXTAY, current_vec_U_chlsk_l_AR1, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, + current_vec_U_chlsk_l_AR1, current_a1, l_idx, n_C, n_T, n_V, n_run, - idx_param_fitV, rank, + n_base, idx_param_fitV, rank, False, False), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, @@ -928,8 +938,10 @@ def _fit_diagV_noGP( res_fitU = scipy.optimize.minimize( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, - n_T, n_V, n_run, idx_param_fitU, rank), + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_logSNR2, l_idx, n_C, + n_T, n_V, n_run, n_base, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 3}) @@ -953,8 +965,8 @@ def _fit_diagV_GP( XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2, current_GP, n_smooth, - idx_param_fitU, idx_param_fitV, - l_idx, n_C, n_T, n_V, n_l, n_run, rank, GP_space, GP_inten, + idx_param_fitU, idx_param_fitV, l_idx, + n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range): """ Last step of fitting. If GP is not requested, it will still fit. @@ -988,18 +1000,24 @@ def _fit_diagV_GP( # fit V rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, \ + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, - X0TY, X0TDY, X0TFY, L, rho1) + X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=( - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, + XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, current_vec_U_chlsk_l_AR1, current_a1, - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, rank, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range), method=self.optimizer, jac=True, @@ -1030,8 +1048,10 @@ def _fit_diagV_GP( res_fitU = scipy.optimize.minimize( self._loglike_AR1_diagV_fitU, param0_fitU, args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, current_logSNR2, l_idx, n_C, n_T, n_V, - n_run, idx_param_fitU, rank), + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_logSNR2, l_idx, n_C, n_T, n_V, + n_run, n_base, idx_param_fitU, rank), method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, @@ -1067,7 +1087,9 @@ def _fit_diagV_GP( def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, - log_SNR2, l_idx, n_C, n_T, n_V, n_run, + X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + log_SNR2, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitU, rank): # This function calculates the log likelihood of data given cholesky # decomposition of U and AR(1) parameters of noise as free parameters. @@ -1099,10 +1121,6 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # Such parametrization avoids the need of boundaries # for parameters. - # n_l = np.size(l_idx[0]) - # the number of parameters in the index of lower-triangular matrix - # This indexing allows for parametrizing only - # part of the lower triangular matrix (non-full rank covariance matrix) L = np.zeros([n_C, rank]) # lower triagular matrix L, cholesky decomposition of U L[l_idx] = param[idx_param_fitU['Cholesky']] @@ -1114,79 +1132,114 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # each element of SNR2 is the ratio of the diagonal element on V # to the variance of the fresh noise in that voxel - YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag - # dimension: space, - # A/sigma2 is the inverse of noise covariance matrix in each voxel. - # YTAY means Y'AY - XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis]\ - * XTDX[np.newaxis, :, :] + rho1[:, np.newaxis, np.newaxis]**2\ - * XTFX[np.newaxis, :, :] - # dimension: space*feature*feature - XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY - # dimension: feature*space - LTXTAY = np.dot(L.T, XTAY) - # dimension: rank*space - # LAMBDA_i = np.zeros([n_V, rank, rank]) - # for i_v in range(n_V): - # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L)\ - # * SNR2[i_v] - # LAMBDA_i += np.eye(rank) - # LTXTAXL = np.empty([n_V, rank, rank]) - # for i_v in range(n_V): - # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) - LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) - LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, \ + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ + self._calc_sandwidge(XTY, XTDY, XTFY, + YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + L, rho1, n_V, n_base) + + # Only starting from this point, SNR2 is involved + LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank - LAMBDA = np.linalg.inv(LAMBDA_i) + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) # dimension: space*rank*rank # LAMBDA is essentially the inverse covariance matrix of the # posterior probability of alpha, which bears the relation with # beta by beta = L * alpha, and L is the Cholesky factor of the # shared covariance matrix U. refer to the explanation below # Equation 5 in the NIPS paper. - YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) - # dimension: space*rank - YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) - # dimension: space*feature (feature can be larger than rank) - # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1)) \ - # / n_T - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ - / n_T - # dimension: space, + # LAMBDA_LTXTAcorrY = np.einsum('ijk,ki->ji', LAMBDA_i, LTXTAcorrY) + YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) + # dimension: space*rank + # # dimension: feature*space + sigma2 = (YTAcorrY - np.sum(LTXTAcorrY * YTAcorrXL_LAMBDA.T, axis=0) + * SNR2) / (n_T - n_base) - LL = -np.sum(np.log(sigma2)) * n_T * 0.5 \ + LL = - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5 \ + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ + - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5 \ - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ - - n_T / 2.0 - # log likelihood - XTAXL = np.dot(XTAX, L) - # dimension: space*feature*rank - deriv_L = -np.einsum('ijk,ikl,i', XTAXL, LAMBDA, SNR2) \ - - np.dot(np.einsum('ijk,ik->ji', XTAXL, YTAXL_LAMBDA) * SNR2**2 - / sigma2, YTAXL_LAMBDA) \ - + np.dot(XTAY / sigma2 * SNR2, YTAXL_LAMBDA) - # - np.einsum('ijk,ik,il,i', XTAXL, YTAXL_LAMBDA, YTAXL_LAMBDA, - # SNR2**2 / sigma2) \ + - (n_T - n_base) * n_V * (1 + np.log(2 * np.pi)) * 0.5 + if not np.isfinite(LL): + print('NaN detected!') + print(sigma2) + print(YTAcorrY) + print(LTXTAcorrY) + print(YTAcorrXL_LAMBDA) + print(SNR2) + + YTAcorrXL_LAMBDA_LT = np.dot(YTAcorrXL_LAMBDA, L.T) + # dimension: space*feature (feature can be larger than rank) + deriv_L = -np.einsum('ijk,ikl,i', XTAcorrXL, LAMBDA, SNR2) \ + - np.dot(np.einsum('ijk,ik->ji', XTAcorrXL, YTAcorrXL_LAMBDA) + * SNR2**2 / sigma2, YTAcorrXL_LAMBDA) \ + + np.dot(XTAcorrY / sigma2 * SNR2, YTAcorrXL_LAMBDA) # dimension: feature*rank + + # The following are for calculating the derivative to a1 + deriv_a1 = np.empty(n_V) dXTAX_drho1 = -XTDX + 2 * rho1[:, np.newaxis, np.newaxis] * XTFX # dimension: space*feature*feature - dXTAY_drho1 = -XTDY + 2 * rho1 * XTFY + dXTAY_drho1 = self._make_sandwidge_grad(XTDY, XTFY, rho1) # dimension: feature*space - dYTAY_drho1 = -YTDY_diag + 2 * rho1 * YTFY_diag - # dimension: space, - deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) * \ - (-n_run * rho1 / (1 - rho1**2) - - np.einsum('...ij,...ji', np.dot(LAMBDA, L.T), - np.dot(dXTAX_drho1, L)) * SNR2 / 2.0 - + np.sum(dXTAY_drho1 * YTAXL_LAMBDA_LT.T, axis=0) - / sigma2 * SNR2 - - np.einsum('...i,...ij,...j', - YTAXL_LAMBDA_LT, dXTAX_drho1, YTAXL_LAMBDA_LT) - / sigma2 / 2.0 * (SNR2**2.0) - - dYTAY_drho1 / (sigma2 * 2.0)) + dYTAY_drho1 = self._make_sandwidge_grad(YTDY_diag, YTFY_diag, rho1) # dimension: space, + dX0TAX0_drho1 = - X0TDX0 \ + + 2 * rho1[:, np.newaxis, np.newaxis] * X0TFX0 + # dimension: space*rank*rank + dXTAX0_drho1 = - XTDX0 \ + + 2 * rho1[:, np.newaxis, np.newaxis] * XTFX0 + # dimension: space*feature*rank + dX0TAY_drho1 = self._make_sandwidge_grad(X0TDY, X0TFY, rho1) + # dimension: rank*space + + # The following are executed for each voxel. + for i_v in range(n_V): + # All variables with _ele as suffix are for data of just one voxel + invX0TAX0_X0TAX_ele = np.dot(X0TAX0_i[i_v, :, :], + XTAX0[i_v, :, :].T) + invX0TAX0_X0TAY_ele = np.dot(X0TAX0_i[i_v, :, :], X0TAY[:, i_v]) + dXTAX0_drho1_invX0TAX0_X0TAX_ele = np.dot(dXTAX0_drho1[i_v, :, :], + invX0TAX0_X0TAX_ele) + # preparation for the variable below + dXTAcorrX_drho1_ele = dXTAX_drho1[i_v, :, :] \ + - dXTAX0_drho1_invX0TAX0_X0TAX_ele \ + - dXTAX0_drho1_invX0TAX0_X0TAX_ele.T \ + + np.dot(np.dot(invX0TAX0_X0TAX_ele.T, + dX0TAX0_drho1[i_v, :, :]), + invX0TAX0_X0TAX_ele) + dXTAcorrY_drho1_ele = dXTAY_drho1[:, i_v] \ + - np.dot(invX0TAX0_X0TAX_ele.T, dX0TAY_drho1[:, i_v]) \ + - np.dot(dXTAX0_drho1[i_v, :, :], invX0TAX0_X0TAY_ele) \ + + np.dot(np.dot(invX0TAX0_X0TAX_ele.T, + dX0TAX0_drho1[i_v, :, :]), + invX0TAX0_X0TAY_ele) + dYTAcorrY_drho1_ele = dYTAY_drho1[i_v] \ + - np.dot(dX0TAY_drho1[:, i_v], invX0TAX0_X0TAY_ele) * 2\ + + np.dot(np.dot(invX0TAX0_X0TAY_ele, dX0TAX0_drho1[i_v, :, :]), + invX0TAX0_X0TAY_ele) + deriv_a1[i_v] = 2 / np.pi / (1 + a1[i_v]**2) \ + * (- n_run * rho1[i_v] / (1 - rho1[i_v]**2) + - np.einsum('ij,ij', X0TAX0_i[i_v, :, :], + dX0TAX0_drho1[i_v, :, :]) * 0.5 + - np.einsum('ij,ij', LAMBDA[i_v, :, :], + np.dot(np.dot( + L.T, dXTAcorrX_drho1_ele), L)) + * (SNR2[i_v] * 0.5) + - dYTAcorrY_drho1_ele * 0.5 / sigma2[i_v] + + SNR2[i_v] / sigma2[i_v] + * np.dot(dXTAcorrY_drho1_ele, + YTAcorrXL_LAMBDA_LT[i_v, :]) + - (0.5 * SNR2[i_v]**2 / sigma2[i_v]) + * np.dot(np.dot(YTAcorrXL_LAMBDA_LT[i_v, :], + dXTAcorrX_drho1_ele), + YTAcorrXL_LAMBDA_LT[i_v, :])) + deriv = np.zeros(np.size(param)) deriv[idx_param_fitU['Cholesky']] = deriv_L[l_idx] deriv[idx_param_fitU['a1']] = deriv_a1 @@ -1194,9 +1247,11 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, return -LL, -deriv def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, - X0TAX0, XTAX0, X0TAY, LTXTAY, + X0TAX0, XTAX0, X0TAY, X0TAX0_i, + XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_l, a1, l_idx, n_C, n_T, n_V, n_run, - idx_param_fitV, rank=None, + n_base, idx_param_fitV, rank=None, GP_space=False, GP_inten=False, dist2=None, inten_dist2=None, space_smooth_range=None, @@ -1248,53 +1303,34 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # If requested, a GP prior is imposed on log(SNR). rho1 = 2.0 / np.pi * np.arctan(a1) # AR(1) coefficient, dimension: space - # YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag - # dimension: space, - # XTAX = XTX[np.newaxis, :, :] - rho1[:, np.newaxis, np.newaxis] \ - # * XTDX[np.newaxis, :, :] \ - # + rho1[:, np.newaxis, np.newaxis]**2 * XTFX[np.newaxis, :, :] - # dimension: space*feature*feature - # XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY - # dimension: feature*space - LTXTAY = np.dot(L.T, XTAY) - # dimension: rank*space - # LAMBDA_i = np.zeros([n_V, rank, rank]) - # for i_v in range(n_V): - # LAMBDA_i[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) \ - # * SNR2[i_v] - # LAMBDA_i += np.eye(rank) - # LTXTAXL = np.empty([n_V, rank, rank]) - # for i_v in range(n_V): - # LTXTAXL[i_v, :, :] = np.dot(np.dot(L.T, XTAX[i_v, :, :]), L) - LTXTAXL = np.tensordot(np.dot(XTAX, L), L, axes=(1, 0)) - LAMBDA_i = LTXTAXL * SNR2[:, None, None] + np.eye(rank) + LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank - LAMBDA = np.linalg.inv(LAMBDA_i) + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) # dimension: space*rank*rank - YTAXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAY) + YTAcorrXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAcorrY) # dimension: space*rank - # YTAXL_LAMBDA_LT = np.dot(YTAXL_LAMBDA, L.T) - # dimension: space*feature - # sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA_LT * XTAY.T, axis=1))\ - # / n_T - sigma2 = (YTAY - SNR2 * np.sum(YTAXL_LAMBDA * LTXTAY.T, axis=1))\ - / n_T + sigma2 = (YTAcorrY + - SNR2 * np.sum(YTAcorrXL_LAMBDA + * LTXTAcorrY.T, axis=1)) / (n_T - n_base) # dimension: space - LL = -np.sum(np.log(sigma2)) * n_T * 0.5\ + LL = - (n_T - n_base) * np.log(2 * np.pi) * 0.5\ + - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5\ + np.sum(np.log(1 - rho1**2)) * n_run * 0.5\ - - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 - n_T * 0.5 + - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5\ + - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5\ + - (n_T - n_base) * n_V * 0.5 # Log likelihood of data given parameters, without the GP prior. deriv_log_SNR2 = (-rank + np.trace(LAMBDA, axis1=1, axis2=2)) * 0.5\ - + YTAY / (sigma2 * 2.0) - n_T * 0.5 \ - - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA, - LTXTAXL, YTAXL_LAMBDA)\ + + YTAcorrY / (sigma2 * 2.0) - (n_T - n_base) * 0.5 \ + - np.einsum('ij,ijk,ik->i', YTAcorrXL_LAMBDA, + LTXTAcorrXL, YTAcorrXL_LAMBDA)\ / (sigma2 * 2.0) * (SNR2**2) - # - np.einsum('ij,ijk,ik->i', YTAXL_LAMBDA_LT, - # XTAX, YTAXL_LAMBDA_LT)\ # Partial derivative of log likelihood over log(SNR^2) # dimension: space, + # The second term above is due to the equation for calculating + # sigma2 if GP_space: # Imposing GP prior on log(SNR) at least over # spatial coordinates @@ -1413,7 +1449,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing, rank=None): # In this version, we assume that beta is independent # between voxels and noise is also independent. @@ -1432,62 +1468,84 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, L = np.zeros([n_C, rank]) L[l_idx] = param[idx_param_sing['Cholesky']] - log_sigma2 = param[idx_param_sing['log_sigma2']] - sigma2 = np.exp(log_sigma2) a1 = param[idx_param_sing['a1']] rho1 = 2.0 / np.pi * np.arctan(a1) XTAX = XTX - rho1 * XTDX + rho1**2 * XTFX - LAMBDA_i = np.eye(rank) +\ - np.dot(np.dot(L.T, XTAX), L) / sigma2 + X0TAX0 = X0TX0 - rho1 * X0TDX0 + rho1**2 * X0TFX0 + XTAX0 = XTX0 - rho1 * XTDX0 + rho1**2 * XTFX0 + XTAcorrX = XTAX - np.dot(XTAX0, np.linalg.solve(X0TAX0, XTAX0.T)) + XTAcorrXL = np.dot(XTAcorrX, L) + LAMBDA_i = np.dot(np.dot(L.T, XTAcorrX), L) + np.eye(rank) XTAY = XTY - rho1 * XTDY + rho1**2 * XTFY - LTXTAY = np.dot(L.T, XTAY) + X0TAY = X0TY - rho1 * X0TDY + rho1**2 * X0TFY + XTAcorrY = XTAY - np.dot(XTAX0, np.linalg.solve(X0TAX0, X0TAY)) + LTXTAcorrY = np.dot(L.T, XTAcorrY) YTAY = YTY_diag - rho1 * YTDY_diag + rho1**2 * YTFY_diag - - LAMBDA_LTXTAY = np.linalg.solve(LAMBDA_i, LTXTAY) - L_LAMBDA_LTXTAY = np.dot(L, LAMBDA_LTXTAY) - - LL = np.sum(LTXTAY * LAMBDA_LTXTAY) / (sigma2**2 * 2.0) \ - - np.sum(YTAY) / (sigma2 * 2.0) - - deriv_L = np.dot(XTAY, LAMBDA_LTXTAY.T) / sigma2**2 \ - - np.dot(np.dot(XTAX, L_LAMBDA_LTXTAY), - LAMBDA_LTXTAY.T) / sigma2**3 - - deriv_log_sigma2 = np.sum(YTAY) / (sigma2 * 2.0) \ - - np.sum(XTAY * L_LAMBDA_LTXTAY) / (sigma2**2) \ - + np.sum(np.dot(XTAX, L_LAMBDA_LTXTAY) - * L_LAMBDA_LTXTAY) / (sigma2**3 * 2.0) + YTAcorrY = YTAY \ + - np.sum(X0TAY * np.linalg.solve(X0TAX0, X0TAY), axis=0) + + LAMBDA_LTXTAcorrY = np.linalg.solve(LAMBDA_i, LTXTAcorrY) + L_LAMBDA_LTXTAcorrY = np.dot(L, LAMBDA_LTXTAcorrY) + + sigma2 = np.mean(YTAcorrY - + np.sum(LTXTAcorrY * LAMBDA_LTXTAcorrY, axis=0))\ + / (n_T - n_base) + LL = n_V * (-np.log(sigma2) * (n_T - n_base) * 0.5 + + np.log(1 - rho1**2) * n_run * 0.5 + - np.log(np.linalg.det(X0TAX0)) * 0.5 + - np.log(np.linalg.det(LAMBDA_i)) * 0.5) + + deriv_L = np.dot(XTAcorrY, LAMBDA_LTXTAcorrY.T) / sigma2 \ + - np.dot(np.dot(XTAcorrXL, LAMBDA_LTXTAcorrY), + LAMBDA_LTXTAcorrY.T) / sigma2 \ + - np.linalg.solve(LAMBDA_i, XTAcorrXL.T).T * n_V + + # These terms are used to construct derivative to a1. + dXTAX_drho1 = - XTDX + 2 * rho1 * XTFX + dX0TAX0_drho1 = - X0TDX0 + 2 * rho1 * X0TFX0 + dXTAX0_drho1 = - XTDX0 + 2 * rho1 * XTFX0 + invX0TAX0_X0TAX = np.linalg.solve(X0TAX0, XTAX0.T) + dXTAX0_drho1_invX0TAX0_X0TAX = np.dot(dXTAX0_drho1, invX0TAX0_X0TAX) + + dXTAcorrX_drho1 = dXTAX_drho1 - dXTAX0_drho1_invX0TAX0_X0TAX \ + - dXTAX0_drho1_invX0TAX0_X0TAX.T \ + + np.dot(np.dot(invX0TAX0_X0TAX.T, dX0TAX0_drho1), + invX0TAX0_X0TAX) + dLTXTAcorrXL_drho1 = np.dot(np.dot(L.T, dXTAcorrX_drho1), L) + + dYTAY_drho1 = - YTDY_diag + 2 * rho1 * YTFY_diag + dX0TAY_drho1 = - X0TDY + 2 * rho1 * X0TFY + invX0TAX0_X0TAY = np.linalg.solve(X0TAX0, X0TAY) + dYTAX0_drho1_invX0TAX0_X0TAY = np.sum(dX0TAY_drho1 + * invX0TAX0_X0TAY, axis=0) + + dYTAcorrY_drho1 = dYTAY_drho1 - dYTAX0_drho1_invX0TAX0_X0TAY * 2\ + + np.sum(invX0TAX0_X0TAY * + np.dot(dX0TAX0_drho1, invX0TAX0_X0TAY), axis=0) + + dXTAY_drho1 = - XTDY + 2 * rho1 * XTFY + dXTAcorrY_drho1 = dXTAY_drho1 \ + - np.dot(dXTAX0_drho1, invX0TAX0_X0TAY) \ + - np.dot(invX0TAX0_X0TAX.T, dX0TAY_drho1) \ + + np.dot(np.dot(invX0TAX0_X0TAX.T, dX0TAX0_drho1), + invX0TAX0_X0TAY) deriv_a1 = 2.0 / (np.pi * (1 + a1**2)) \ - * (-n_run * rho1 / (1 - rho1**2) - + np.sum((-XTDY + 2 * rho1 * XTFY) - * L_LAMBDA_LTXTAY) / (sigma2**2) - - np.sum(np.dot((-XTDX + 2 * rho1 * XTFX), L_LAMBDA_LTXTAY) - * L_LAMBDA_LTXTAY) / (sigma2**3 * 2.0) - - np.sum(-YTDY_diag + 2 * rho1 * YTFY_diag) / (sigma2 * 2.0)) - - LL = LL + np.size(YTY_diag) * (-log_sigma2 * n_T * 0.5 - + np.log(1 - rho1**2) * n_run * 0.5 - - np.log(np.linalg.det(LAMBDA_i)) - * 0.5) - - deriv_L = deriv_L - np.linalg.solve(LAMBDA_i, np.dot(L.T, XTAX)).T\ - / sigma2 * np.size(YTY_diag) - deriv_log_sigma2 = deriv_log_sigma2 \ - + (rank - n_T - np.trace(np.linalg.inv(LAMBDA_i)))\ - * 0.5 * np.size(YTY_diag) - deriv_a1 = deriv_a1 - np.trace( - np.linalg.solve(LAMBDA_i, - np.dot(np.dot(L.T, - (-XTDX + 2 * rho1 * XTFX)), L)))\ - / (sigma2 * 2) * np.size(YTY_diag) + * (n_V * (- n_run * rho1 / (1 - rho1**2) + - 0.5 * np.trace(np.linalg.solve( + X0TAX0, dX0TAX0_drho1)) + - 0.5 * np.trace(np.linalg.solve( + LAMBDA_i, dLTXTAcorrXL_drho1))) + - 0.5 * np.sum(dYTAcorrY_drho1) / sigma2 + + np.sum(dXTAcorrY_drho1 * L_LAMBDA_LTXTAcorrY) / sigma2 + - 0.5 * np.sum(np.dot(dXTAcorrX_drho1, L_LAMBDA_LTXTAcorrY) + * L_LAMBDA_LTXTAcorrY) / sigma2) deriv = np.zeros(np.size(param)) - deriv[0:n_l] = deriv_L[l_idx] - deriv[n_l] = deriv_log_sigma2 - deriv[n_l + 1] = deriv_a1 + deriv[idx_param_sing['Cholesky']] = deriv_L[l_idx] + deriv[idx_param_sing['a1']] = deriv_a1 return -LL, -deriv diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index aa96a5f06..187727706 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -1,8 +1,12 @@ { "cells": [ { - "cell_type": "markdown", - "metadata": {}, + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], "source": [ "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset." ] @@ -16,7 +20,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "collapsed": false }, @@ -32,7 +36,7 @@ "import numdifftools as nd\n", "import matplotlib.pyplot as plt\n", "import logging\n", - "np.random.seed(100)" + "np.random.seed(10)" ] }, { @@ -44,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": { "collapsed": false }, @@ -80,22 +84,11 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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9vXHs2DGEhIT87Xnp4+HhAa1Wi7Nnz6ruSN26dQuZmZlP1eaOHz+Os2fPYvHi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\nSUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "design = utils.ReadDesign(fname=\"example_design.1D\")\n", "\n", @@ -107,7 +100,7 @@ "fig = plt.figure(num=None, figsize=(12, 3), dpi=150, facecolor='w', edgecolor='k')\n", "\n", "plt.plot(design.design_used)\n", - "plt.ylim([-0.2,1.2])\n", + "plt.ylim([-0.2,0.4])\n", "plt.title('hypothetic fMRI response time courses of all conditions in addition to a DC component\\n'\n", " '(design matrix)')\n", "plt.xlabel('time')\n", @@ -133,22 +126,11 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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PwohPZnR0mKvhqSLdPDD5uT6eNHd2uk+gE91x8zNge3lmJpCeHvsAt3Ah8N57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\nLFvMVdIddvZydQ9YwLSY+1G67bKXq0p3Xp7Vos6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p5u/q9vKwlG4n0q3vHKRCn0+rSndb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\n9ttv47DDDnP9bWHhPAwatBjAYsyfvxiLFy/GrFmzLErQpk00ELByaGf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I6C4tSlJ0n3km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\nt0ac7vIjFtG9ePFiL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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "noise_bot = 0.5\n", "noise_top = 1.5\n", @@ -169,6 +151,7 @@ "for i_t in range(1,n_T):\n", " noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", "# Here, we assume noise is independent between voxels\n", + "noise = noise + np.random.randn(n_V)\n", "fig = plt.figure(num=None, figsize=(12, 2), dpi=150, facecolor='w', edgecolor='k')\n", "plt.plot(noise[:,0])\n", "plt.title('noise in an example voxel')\n", @@ -199,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": { "collapsed": false }, @@ -224,39 +207,17 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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AiaSud99Hb2bWjwJXGTuPNKV1IRunjI0GZgJIOgsYHxFHZY8/ASwlxbZtSGO6\n+wNvb7ZdRQTdjwNnAhcCLyB91H0jSzMzy62oRcwjYrakMcAZpGGFxcCUiHg0yzIO2LGuyFakeb3j\ngdXALcDkiPhVs+1qe9CNiKeAT2WbmdmgFXkZcETMAGb08dwxDY+/DHw5V0MaeO0FM6s8L2JuZmYt\ncU/XzCqvKvN028FB18wqr3YZcN4yVeSga2aV183IFi4DrmZ4q2arzMzq+HY9ZmYl8uwFMzNriXu6\nZlZ5nr1gZlYiz14wMytRQYuYDwkH3WFqMGviej1cK5uHF8zMSuTZC2Zm1hL3dM2s8opaT3coOOia\nWeUVuZ5u2Rx0zazyOmlM10HXzCqvk2YvVPOjwMysQ7mna2aV10lXpBXSKknjJX1X0kpJqyXdLGli\nEXWZWeerXZGWb2suSEs6UdJSSWskLZC0V5Pl9pG0TtKiPMfS9qAraQfgBuBpYArwKuDTwF/bXZeZ\nDQ+1Md08WzNjupIOI91S/TRgD+BmYF52W/b+yj0HuBSYn/dYihheOBl4ICKOr0u7v4B6zGyYKHAR\n82nARRExC0DSVOBg4FjgnH7KfRP4HtADvCtPu4oYXjgE+L2k2ZJWSFok6fgBS5mZ9SFvL7e29UfS\nKGAScG0tLSKC1Hvdu59yxwAvBb7QyrEUEXQnAB8D/gQcAHwDmC7pnwqoy8ysVWOALmBFQ/oKYFxv\nBSS9AvhP4IMR0dNKpUUML4wAboqIU7PHN0t6LTAV+G4B9ZlZh6vC7AVJI0hDCqdFxD215Lz7KSLo\nPgIsaUhbAry3/2JzgW0a0nbNNms0mKUZwcszWhFuzbZ6a9uy54HW01112VyeuGzupmVWPTnQblcC\n3cDYhvSxwPJe8j8b2BPYXdKFWdoIQJKeAQ6IiF8MVGkRQfcGYJeGtF0Y8GTagcD4AppjZuXorZO0\nDLh40Hse6Iq07Y44mO2OOHiTtLWLlvDApMP7LBMR6yQtBCYDcyBFz+zx9F6KPAG8tiHtRGB/4B+B\n+wY6Digm6H4VuEHS54DZwBuA44F/LqAuMxsGCpy9cB4wMwu+N5FmM4wGZgJIOgsYHxFHZSfZbq8v\nLOnPwNqIaPx236e2B92I+L2k9wBnA6cCS4FPRMQP2l2XmQ0P6xlBV86gu76JoBsRs7M5uWeQhhUW\nA1Mi4tEsyzhgx3yt7V8hlwFHxNXA1UXs28ysnSJiBjCjj+eOGaDsF8g5dcxrL5hZ5fVkl/bmLVNF\n1WyVmVn+jKn+AAAPpklEQVSdAsd0S+ega2aV180IRnTIKmMOumZWeT09XXT35Ozp5sxfFgddM6u8\n7u4RsD5nT7e7mj3darbKzKxDuadrZpXXvb4L1ucLV905e8ZlcdA1s8rr6e7KPbzQ0+2ga2bWku7u\nEUTuoFvN0VMHXTOrvO71XfSsyxd08wbpslTzo8DMrEO5pzuEBrMmrtfDteEkerqI7pzhyvN0zcxa\ntD7/PF3WV/OLvIOumVVfC7MX8OwFM7MWdQvW57wdWXfu25eVwkHXzKqvG1jfQpkKquagh5lZh3JP\n18yqr4N6ug66ZlZ968kfdPPmL4mDrplV33pgXQtlKqjwMV1JJ0vqkXRe0XWZWYfqIQ0X5Nl6mtu1\npBMlLZW0RtICSXv1k3cfSb+WtFLSaklLJH0yz6EU2tPNGv8R4OYi6zGzDlfQmK6kw4BzSXHqJmAa\nME/SzhGxspciTwFfA27Jfn8zcLGkJyPi2800q7CerqTtgP8GjgceL6oeM7NBmAZcFBGzIuIOYCqw\nGji2t8wRsTgifhgRSyLigYj4PjAP2LfZCoscXrgQuDIifl5gHWY2HKxvceuHpFHAJODaWlpEBDAf\n2LuZZknaI8v7i2YPpZDhBUmHA7sDexaxfzMbZooZXhgDdAErGtJXALv0V1DSg8Dzs/KnR8R3mm1W\n24OupBcD5wNvi4i85xvNzDZXvXm6bwa2A94IfEnS3RHNLRtYRE93EukTYJGk2sXPXcBbJH0c2Drr\nwjeYC2zTkLZrtlXTYJZmBC/PaJ3m1myrt7Y9ux4o6P7qsrTVW71qoL2uzPY8tiF9LLC8v4IRcX/2\n622SxgGnA0MWdOezeaScCSwBzu494AIcCIwvoDlmVo7eOknLgIsHv+uBgu6bjkhbvXsXwb9N6rNI\nRKyTtBCYDMwByDqKk4HpOVrXBWzdbOa2B92IeAq4vT5N0lPAXyJiSbvrMzMbhPOAmVnwrU0ZG03q\nKCLpLGB8RByVPT4BeAC4Iyu/H/Bp0pBqU8q6Iq2P3q2ZWRMKuiItImZLGgOcQRpWWAxMiYhHsyzj\ngB3riowAzgJ2ymq4B/i3iGi6O19K0I2IfyijHjPrULWrzPKWaUJEzABm9PHcMQ2Pvw58PWdLNuG1\nF8ys+qo3e6FlDrpmVn0dFHS9iLmZWYnc0zWz6uugnq6DrplVnxcxNzMrkXu6ZmYlctA1MyuRb9dj\nZmatcE/XzKqvwCvSyuaga2bV5zHdzjGYNXG9Hq5ZSRx0zcxK5KBrZlYiz14wM7NWuKdrZtXn2Qtm\nZiXymK6ZWYkcdM3MStRBJ9IcdM2s+jpoTLftsxckfU7STZKekLRC0v9K2rnd9ZiZtYOkEyUtlbRG\n0gJJe/WT9z2SrpH0Z0mrJP1G0gF56itiyti+wNeANwBvA0YB10h6VgF1mdlwUBvTzbM10dOVdBhw\nLnAasAdwMzAvuy17b94CXAMcBEwErgOulLRbs4fS9uGFiHhH/WNJRwN/BiYBv253fWY2DBR3Im0a\ncFFEzAKQNBU4GDgWOKcxc0RMa0j6vKR3AYeQAvaAyrg4YgcggMdKqMvMOlHtRFqebYAgLWkUqTN4\nbS0tIgKYD+zdTLMkCXg2OeJboSfSsgadD/w6Im4vsi4z62A95D8x1jNgjjFAF7CiIX0FsEuTtfwb\nsC0wu9lmFT17YQbwamCfgusxMyuVpCOBU4FDI2Jls+UKC7qSvg68A9g3Ih4ZuMRcYJuGtF2zrW+D\nWZoRvDyjWfvcmm311rZn1wPdDfjhy9JWb92qgfa6ktR/HtuQPhZY3l9BSYcDFwPvi4jrBqqoXiFB\nNwu47wL2i4gHmit1IDC+iOaYWSl66yQtI8WmQRroRNrYI9JWb9Ui+M2kPotExDpJC4HJwBzYMCQ6\nGZjeVzlJRwDfBg6LiLlNHsEGbQ+6kmYARwCHAk9Jqn2KrIqINn3smdmwUtwVaecBM7PgexNpNsNo\nYCaApLOA8RFxVPb4yOy5k4Df1cW3NRHxRDMVFtHTnUqarfCLhvRjgFkF1Gdmna6YE2lExOxsTu4Z\npGGFxcCUiHg0yzIO2LGuyD+TTr5dmG01l5KmmQ2oiHm6XqPXzNqrwAVvImIG6aR/b88d0/B4/5yt\n2IwDpJlZibzgjZlV30CzF/oqU0EOumZWfV7a0cysRAWdSBsKDrpmVn2+c4SZWYk6aEzXsxfMzErk\nnq6ZVZ9PpJmZlcgn0szMSuQTaWZmJXLQLcIHgd1zl5qo9rfEzCqmlfHZio7pevaCmVmJKtTTNTPr\nQzeQ91uthxfMzFrUSgB10DUza1E36dYIeXjKmJlZi9aTf3ghb5AuiU+kmZmVyD1dM6u+Vk6kVbSn\n66BrZluGigbRvAobXpB0oqSlktZIWiBpr6LqGpxbXbfrdt3DWJ5YJWmcpO9J+pOkbknn5a2vkKAr\n6TDgXOA0YA/gZmBedqvjihmu/wiu23VbC7Fqa+DPwJmk27XnVlRPdxpwUUTMiog7gKnAapq8L7yZ\nWUlyxaqIuD8ipkXEfwNPtFJh24OupFHAJODaWlpEBDAf2Lvd9ZmZtWKoYlURJ9LGAF3Aiob0FcAu\nBdRnZh2vkFXMhyRWVWH2wjbpx50tFl82yOrXtmEfrtt1u+7eraz9ss3g9tM5N0krIuiuJM2qG9uQ\nPhZY3kv+ndKPfy6gKc262HW7btddrJ2A37RefKCe7o+yrd6qgXaaN1a1RduDbkSsk7QQmAzMAZCk\n7PH0XorMIy2mex/p49jMOsc2pIA7b3C7GWgV83dnW72bgX/os0QLsaotihpeOA+YmR3QTaQzhKOB\nmY0ZI+IvwPcLaoeZDb1B9HBrCrszZb+xStJZwPiIOKpWQNJupOvjtgOenz1+JiKWNFNhIUE3ImZn\n89zOIHXVFwNTIuLRIuozM2tFE7FqHLBjQ7E/sPH6uInAkcD9wIRm6lSaIWFmVj2SJgIL4Wpg15yl\nbwXeATApIha1u22tqsLsBTOzAXTOnSkddM1sC1DYmG7phnw93aFYGEfS5yTdJOkJSSsk/a+knYuu\nt4+2nCypp5WFM1qsb7yk70paKWm1pJuzr3BF1ztC0pmS7s3qvVvSKQXVta+kOZIezl7bQ3vJc4ak\nZVlbfibp5UXXLWmkpC9JukXSk1meSyW9sOi6e8n7zSzPSWXVLelVkq6Q9Hh2/DdKenFzNdR6unm2\navZ0hzToDuHCOPsCXwPeALwNGAVcI+lZBde7iewD5iOk4y6jvh2AG4CngSnAq4BPA38tofqTgY8C\nJwCvBD4DfEbSxwuoa1vSCZET6GVBQEmfBT5Oeu1fDzxFet9tVXDdo4HdgS+Q3u/vIV35dEUb6h2o\n7g0kvYf03n+4TfUOWLeklwHXA7cDbyEN0J5J09NEaz3dPFs1e7pExJBtwALggrrHAh4CPlNyO8aQ\n7qj05hLr3A74E2ki4XXAeSXUeTbwyyH6W18JfKsh7UfArILr7QEObUhbBkyre7w9sAb4QNF195Jn\nT1KX7MVl1A28CHiA9IG7FDippNf8MuDSFvY1EQj4QcDNObcfRCrLxCLfY3m3IevpVmxhnB1If5zH\nSqzzQuDKiPh5iXUeAvxe0ux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axHxYOOiOUENZ09br4VrZPL1gZlYiZy+YmVlbPNI1s8oraj3d4eCga2aVV+R6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\nPR07VKOA6yPi1OzxjZJeRVp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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# ideal covariance matrix\n", "ideal_cov = np.zeros([n_C,n_C])\n", "ideal_cov = np.eye(n_C)*0.6\n", - "ideal_cov[0,0] = 0.1\n", - "ideal_cov[9:13,9:13] = 0.8\n", - "for cond in range(9,13):\n", + "ideal_cov[8:12,8:12] = 0.8\n", + "for cond in range(8,12):\n", " ideal_cov[cond,cond] = 1\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", @@ -291,49 +252,18 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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AEBAQAJ7nMX78eHTs2FHnYKcsOTg4AACePn2KmjVrit57+vSp1oH1ClNPl2Zn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FvONxWB0IxUOGd33Pp9vTrYxn4/mAEH0Qc9QzcgYjU1mjQzehHjWHUdmKUKjPou7aXMhRD8aC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\n9u3bTVZW1pT3k5KSzM6dO/2fDw4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gQQYAV18NfOc7wK5d3rZH8Ad791JlcqNVy0RUivYj0YS+64V6Vxf9/7Zt9NjI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\n0TvqeXn2awyJUBe0iFCPE23oe0kJXYx6V0+b6+y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kCGnDkSIJ9WRy1K2E+u7dobm6ZkJd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AewfAv1QYPIJcxVqLuVZ+vtpZDMQnDUUyngy18G/u3fjMRydvvUc80SW1MTXjK5fDjqhw8HdzYu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\nQm9vr+v/3nnnnRg1ahRqampw4YUXoqWlJ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4G4AtR/JaZjZxDIxeaOeoa0t3pD8K1qB0OTQP4HuyeszMbELzkDEzqz3PSBva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\n13AkbS3pQkmPVvXdZZCYI6u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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "\n", "\n", "L_full = np.linalg.cholesky(ideal_cov) \n", "\n", "# generating signal\n", - "snr_level = 0.5\n", + "snr_level = 0.6\n", "# Notice that accurately speaking this is not snr. the magnitude of signal depends\n", "# not only on beta but also on x. (noise_level*snr_level)**2 is the factor multiplied\n", "# with ideal_cov to form the covariance matrix from which the response amplitudes (beta)\n", @@ -377,7 +307,7 @@ "signal = np.dot(design.design_used,betas_simulated)\n", "\n", "\n", - "Y = signal + noise\n", + "Y = signal + noise \n", "# The data to be fed to the program.\n", "\n", "\n", @@ -422,19 +352,11 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "scan onsets: [ 0. 186.]\n" - ] - } - ], + "outputs": [], "source": [ "scan_onsets = np.linspace(0,design.n_TR,num=n_run+1)[:-1]\n", "print('scan onsets: {}'.format(scan_onsets))" @@ -449,25 +371,11 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "BRSA(GP_inten=True, GP_space=True, epsilon=0.0001, init_iter=20,\n", - " inten_smooth_range=None, n_iter=50, optimizer='BFGS', pad_DC=False,\n", - " rand_seed=0, rank=None, space_smooth_range=None, tau_range=10,\n", - " tol=0.002, verbose=False)" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "brsa = BRSA(GP_space=True,GP_inten=True,tau_range=10)\n", "# Initiate an instance, telling it that we want to impose Gaussian Process prior over both space and intensity.\n", @@ -487,32 +395,11 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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XqH9yzFcIoTE/E+t9lDBbPddCxpgCF7M4L2I13GVmDybG/wJwDbBt4jF/Z0KM6Y7UmP5K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\ntjE0deYcc3HtS0j94jiOUx9taHNu2sx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7AFsDT7dWNeecc41oumulkcnYJb0bOA3YHbgyTwWdc877yLO1vY88BvdzgVPM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\nAprggdw5V3qV2+6bzVOPmV0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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(brsa.C_, vmin=-0.1, vmax=1)\n", @@ -546,36 +433,16 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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tVKXJAcA44D3x7/uAl1k0iWZ/3F/a3p/mMEs0Esd8ExkMem2/suM4Tgpa52Oe\nCJxuZucCSNoH2A7YEziuvLKZvQ68Xvos6cvA8sCURavaixk1fps2XhjPcZyOoQWuDEljgG7g+lKZ\nmRlwHbBZSs32BK4zs6fLypeWNEPSU5IulbRuyv4AN8yO43QuKxHM98yy8pkE90NNJL0H2BY4o2zX\nIwSDvQPwTYKdvU3SqmkV89XlHMcpPnVcGb3/CluS/nkt1QjgO8ArwGXJQjO7A7ij9FnS7cA04Puk\nCwl3w+w4ThtQxzD3bBC2JH3PQfdpNXudBQwAq5SVrwK8kEKrPYBzzWxBrUpmtkDSPWSYqOGuDMdx\nik8LojLMbD4humyrUllc62cr4LZabSV9Gvgg8Pt6qksaBawHPF+vbgkfMTuOU3xat4jRCcAUSVOB\nuwhRGmOJURaSjgVWNbPdy9p9F7jTzBZZn0DS4QRXxmOEiI2DgNWBM9Oq7obZcZzi06JwOTO7MMYs\nH0VwYdwLbJMIdRsHrJZsI2lZYCdCTHMlVgB+F9u+QhiVb2ZmD6dV3Q2z4zgdjZlNBiZX2bdHhbLX\nqLGklZkdCByYRyc3zI7jFB9fxMhxHKdg+EL5I8WywLsaaLdtsxVJz/apQhKrk+vsj88nm7sab7pC\njrWcITGhtQGOqLYkS0q2zfGdXf1yLtGTyDT5q6ztQ7lk51+3/HM52+fER8yO4zgFww2z4zhOwRhF\ndkPbxrM02lh1x3GcxRMfMTuOU3xKs/mytmlT2lh1x3E6BvcxO47jFAw3zI7jOAWjw17+uWF2HKf4\ndJiPuY3vKY7jOIsnmQ2zpC0kXS7p2ZiWe4fEvtGSfinpfklvxDrnxBQsjuM4jdGiLNlFpZER81KE\npfH2Baxs31hgA+BIQirwnYB1KEu94jiOk4mSjznL1sb+gMxeGDO7BrgG3l7tP7nvNWCbZJmk/YE7\nJb3PzJ7JoavjOJ2KR2U0neUJI+tXh0GW4ziLI/7yr3lIWhL4BXC+mb3RSlmO4ziLCy27p0gaDVxE\nGC3vW7fBkmdB13JDy5bqgaV7arf7QqMaRv6Wo+0VOZegzKX8IqnGMrJD/SrVeCWn6Acbb/rVdVMn\nGq7IxX2Nt5109Yq5ZE/ipcYbr9bIkrgJ3piQr30Kent76e3tHVLW39/fnM49jjk/CaO8GvDZVKPl\nFU+EJTdqhTqO4wwDPT099PQMHUj19fXR3d2dv3P3MecjYZTXAD5jZnnHV47jdDod5mPOrLqkpYA1\ngVJExho3u17nAAAeQElEQVSS1gdeBp4HLiaEzH0JGCNplVjvZTObn19lx3E6Dh8x12Vj4AaC79iA\n42P5OYT45e1j+b2xXPHzZ4B/5FHWcZwOxX3MtTGzm6h9yG18OhzHcUaeNvbCOI7TMbgrw3Ecp2D4\nyz/HcZyC4T5mx3GcguGuDMdxnILRYYa5jQf7juM4iyc+YnYcp/j4yz/HcZxiYaPAMromrI39AW2s\nuuM4ncJAFwyMzrilNOSS9pM0XdJcSXdI+lid+ktIOkbSDEnzJD0h6Ttldb4maVrs8z5J22Y5Xh8x\nO45TeAajYc7aph6SdiEsK7E3cBcwEbhW0tpmNqtKs4uAlYE9gMeB95AY5Er6BHA+cDBwJfBN4FJJ\nG5rZQ2l0L45hfm4eMDd7u7+8M5/cp+9vvO0yR+ST/fqfcjR+Xz7Z5Dhu3ptP9HVrNdz04hO/mUv0\npDNVv1K1tlPLU1xm5LAcbfOsGw6w4M6cHWyas30+BrrEgq5s391AV2k5n5pMBE43s3MBJO0DbAfs\nCRxXXlnSF4AtgDXMrJSV6amyagcAV5vZCfHzzyRtDexPmrXpcVeG4zgdiqQxQDdwfanMzAy4Dtis\nSrPtgbuBgyU9I+kRSf8r6R2JOpvFPpJcW6PPRSjOiNlxHKcKA11dDIzONo4c6BoEFtSqshIh2nlm\nWflMYJ0qbdYgjJjnAV+OffwWeBfw3VhnXJU+x6VU3Q2z4zjFZ7Cri4GubIZ5sEvUMcyNMAoYBHYt\nZWaSdCBwkaR9zezNZghxw+w4TuEZYBQDNabyXdI7n0t6hxrh1/rr+pdnAQPAKmXlqwAvVGnzPPBs\nWbq8aYR1599HeBn4QsY+F8ENs+M4hWeALhbUMMw79HSxQ1ne5vv7Btimu3q6UTObL2kqsBVwOYAk\nxc8nV2l2K7CzpLFmNieWrUMYRT8TP99eoY+tY3kq/OWf4zidzAnA9yTtJulDwGnAWGAKgKRjJZ2T\nqH8+8BJwtqQJkj5FiN74fcKNcRLwBUkHSlpH0iTCS8ZT0yrlI2bHcQrPIF0MZDRXgynqmNmFklYC\njiK4G+4FtjGzF2OVccBqifqzY+jbKcA/CUb6T8DhiTq3S9oVOCZujwI7po1hBjfMjuO0AfV8zJXb\npDHNYGaTgclV9u1RoezfwDZ1+ryYkJi6IdwwO45TeMKIOZthHkxpmItIZh+zpC0kXS7pWUmDknao\nUOcoSc9JmiPpb5LWbI66juN0IoNxxJxlG2zjV2iNaL4UwQ+zLxXmO0o6mDD1cG9gE2A2Ye75Ejn0\ndByng1nAKBbEyIz0W/sa5syuDDO7BrgG3g4tKedHwNFm9pdYZzfCrJcvAxc2rqrjOE5n0NRbiqQP\nEN5iJueevwbcSYZ54o7jOEkGGc1Axm2wjV+hNVvzcQT3Rq554o7jOEkGG4jKaGcfc4FuKYcCy5WV\n9cStBk8fmU/sHjmW7jz7t/lk5+LhnO33ydH25VySl/jWaw23/cmK5ddINibt1fjSnV/d6I+5ZF98\n9WONNz4y5xKz97Z+2c7e3l56e3uHlPX39zel78bC5dwwl3iBMGd8FYaOmlcB7qnd9ERgoyar4zjO\ncNHT00NPz9CBVF9fH93d3bn7rjclu1qbdqWptxQzm04wzluVyiQtS1hl+7ZmynIcp3MozfzL5mNu\nX8OcecQsaSlgTcLIGGANSesDL5vZ08CvgcMkPQbMAI4mLO5xWVM0dhzHWcxpxJWxMXAD4SWfEfJl\nAZwD7Glmx0kaC5wOLA/cDGxrZm81QV/HcTqQ0qSRrG3alUbimG+ijgvEzCYBkxpTyXEcZygeleE4\njlMwPCrDcRynYHRaVIYbZsdxCk9j6zG3r2Fu37G+4zjOYoqPmB3HKTzuY3YcxykYjS2U376uDDfM\njuMUnoG4HnPWNu2KG2bHcQrPQAMv/9o5KqN9bymO4ziLKT5idhyn8LiPecR4iUXX10/DxHxiz87T\neJd8ssmznvPuOWXnyfK1Vy7JP1lxbMNtf/5SzvV9z2u86cUPfTOf7Dy/tl/lE833c7YfYTwqw3Ec\np2D4zD/HcZyC0Wkz/9wwO45TeDrNldG+mjuO4yym+IjZcZzC41EZjuM4BcMXynccxykYCxqIysha\nv0i4YXYcp/B4VIbjOE7B8KiMnEgaJeloSU9ImiPpMUmHNVuO4zhOM5C0n6TpkuZKukPSx1K221zS\nfEl9ZeW7SxqUNBD/Dkqak0WnVoyYDyFMAN0NeAjYGJgi6VUzO7UF8hzHWcxpVVSGpF2A44G9gbsI\nazxcK2ltM5tVo91ywDnAdcAqFar0A2sDip8ti+6tMMybAZeZ2TXx81OSdgU2aYEsx3E6gBauxzwR\nON3MzgWQtA+wHbAncFyNdqcBfwQGgR0r7DczezGTwgla4YS5DdhK0loAktYHNgeuaoEsx3E6gNJ6\nzNm22oZc0higG7i+VGZmRhgFb1aj3R7AB4Aja3S/tKQZkp6SdKmkdbMcbytGzL8AlgUeljRAMP4/\nNbMLWiDLcZwOoEWujJWALhZd1nImsE6lBnHA+XPgk2Y2KKlStUcII+77geWA/wZuk7SumT2XRvdW\nGOZdgF2BbxB8zBsAJ0l6zsz+ULXVEv8Do5YbWja2B5bqqS1tpXzKck+expn8+RU4KEfbZ/OJXu2H\nDTed9HTFizF9+zznbcUZuWQ3trRsibXyiV4hR9tXpuWT/eCEfO1T0NvbS29v75Cy/v6cy7RG6k0w\nebD3XzzU+68hZfP632yK7BKSRhHcF0eY2eOl4vJ6ZnYHcEei3e3ANMK7tyPSyGqFYT4OONbMLoqf\nH5Q0HjgUqG6YVzgRltioBeo4jjMc9PT00NMzdCDV19dHd3d3y2V/uOcjfLjnI0PKXuh7nrO6z6zV\nbBYwwKIv71YBXqhQfxlCMMMGkn4Ty0YBkvQW8Hkzu7G8kZktkHQPsGaKQ3m702YzlnCwSQZbJMtx\nnA6gFMecbattcsxsPjAV2KpUpuCb2Irwrqyc14CPELwA68ftNODh+P+dleTEkfZ6wPNpj7cVI+Yr\ngMMkPQM8CGxEePNZ89blOI5TjRYulH8CIZx3KgvD5cYCUwAkHQusama7xxeDDyUbS/oPMM/MpiXK\nDie4Mh4Dlif4LFcngw1shWHeHzga+A3wbuA5Qg6lo1sgy3GcDqBVU7LN7EJJKwFHEVwY9wLbJELd\nxgGrZdOWFYDfxbavEEblm5nZw2k7aLphNrPZwIFxcxzHyU0rp2Sb2WRgcpV9e9RpeyRlYXNmltv+\nud/XcRynYPgiRo7jFB5fKN9xHKdgtHBKdiFxw+w4TuEpTbPO2qZdaV/NHcfpGDy1lOM4TsHwhfId\nx3GcEcVHzI7jFB6PynAcxykYHpXhOI5TMAYamJKddYRdJIpjmGdRYWXTFCyfV/AVOdqul0/0XmMa\nb/un8blE51lTedJqmdKXLcrTp+Ro/PV8ssmzrvGK+US/cmuOxjmvtavznHOAxtfvbgbuynAcxykY\nHpXhOI7jjCg+YnYcp/C0cD3mQuKG2XGcwtOq9ZiLihtmx3EKT6f5mN0wO45TeDotKqN9bymO4ziL\nKT5idhyn8PjMP8dxnILRaTP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dC/tpnZ+tlf2sYllSQ3RtYBFwE7BDRHS9wdnH03yY2cDoUVdGRPyhUcqI2Lfm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\nubCLgNfX7DuVtFTLMfWDspm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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "betas_point = np.linalg.lstsq(design.design_used, Y)[0]\n", - "point_corr = np.corrcoef(betas_point)\n", - "point_cov = np.cov(betas_point) \n", + "regressor = np.insert(design.design_used,0,1,axis=1)\n", + "betas_point = np.linalg.lstsq(regressor, Y)[0]\n", + "point_corr = np.corrcoef(betas_point[1:,:])\n", + "point_cov = np.cov(betas_point[1:,:])\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(point_corr, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", @@ -608,32 +475,11 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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1u9T+4xh+vfNtrL1+9XCG/45p2AaySNpf0s8lPSlpQNK7ql7/frG98nF1bjtm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\nMDEz/tLMb8MvKvGR8Td54Rv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Z8TXq4AUMLZOMzMysHx38nVGL5kgzMxtOPDIyM2sXHTwycjIyM2sXXk1nZmY2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\n4y/7zUIXdu7XZw+7Km+Hbc/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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "fig = plt.figure(num=None, figsize=(5, 5), dpi=100)\n", "plt.pcolor(np.reshape(brsa.nSNR_, [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", @@ -654,23 +500,11 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "RMS error of Bayesian RSA: 0.13665981702261623\n", - "RMS error of standard RSA: 0.1433569522028947\n", - "Recovered spatial smoothness length scale: 5.595133988654466, vs. true value: 3.0\n", - "Recovered intensity smoothness length scale: 4.611783121422689, vs. true value: 4.0\n", - "Recovered standard deviation of GP prior: 0.184521447350508, vs. true value: 0.8\n" - ] - } - ], + "outputs": [], "source": [ "RMS_BRSA = np.mean((brsa.C_ - ideal_corr)**2)**0.5\n", "RMS_RSA = np.mean((point_corr - ideal_corr)**2)**0.5\n", @@ -687,6 +521,31 @@ "source": [ "#### Empirically, the smoothness turns to be over-estimated when signal is weak." ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.scatter(brsa.sigma_, noise_level)\n", + "plt.show()\n", + "plt.scatter(brsa.rho_, rho1)\n", + "plt.show()\n", + "plt.scatter(brsa.nSNR_, snr)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index e487db9b0..903a9b3a3 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -27,7 +27,7 @@ def test_can_instantiate(): features = 3 s = brainiak.reprsimil.brsa.BRSA(n_iter=50, rank=5, GP_space=True, GP_inten=True, tol=2e-3,\ - pad_DC=False,epsilon=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) + epsilon=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) assert s, "Invalid BRSA instance!" def test_fit(): @@ -70,7 +70,6 @@ def test_fit(): # ideal covariance matrix ideal_cov = np.zeros([n_C,n_C]) ideal_cov = np.eye(n_C)*0.6 - ideal_cov[0,0] = 0.2 ideal_cov[5:9,5:9] = 0.6 for cond in range(5,9): ideal_cov[cond,cond] = 1 @@ -133,7 +132,28 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" - + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + + # Test fitting with lower rank + rank = n_C - 1 + brsa = BRSA(rank=rank) + brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, + coords=coords, inten=inten) + u_b = brsa.U_[1:,1:] + u_i = ideal_cov[1:,1:] + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" + # check that the recovered SNRs makes sense + p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] + assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" # Test fitting without GP prior. brsa = BRSA() @@ -148,6 +168,10 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" assert not hasattr(brsa,'bGP_') and not hasattr(brsa,'lGPspace_') and not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of GP if GP is not requested.' # GP parameters are not set if not requested @@ -164,6 +188,10 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" + p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] + assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" assert not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of lGPinten_ if only smoothness in space is requested.' # GP parameters are not set if not requested @@ -252,12 +280,12 @@ def test_gradient(): # Test fitting with GP prior. - brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) + brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,rank=n_C) # test if the gradients are correct XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run_returned =\ + X0TY, X0TDY, X0TFY, X0, n_run_returned, n_base =\ brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ @@ -274,12 +302,15 @@ def test_gradient(): 'Dimension of X0TY etc. returned from _prepare_data is wrong' X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) + # rank = n_C - 1 + # idx_rank = np.where(l_idx[1] < rank) + # l_idx = (l_idx[0][idx_rank], l_idx[1][idx_rank]) n_l = np.size(l_idx[0]) # Make sure all the fields are in the indices. idx_param_sing, idx_param_fitU, idx_param_fitV = brsa._build_index_param(n_l, n_V, 2) - assert 'Cholesky' in idx_param_sing and 'log_sigma2' in idx_param_sing \ - and 'a1' in idx_param_sing, 'The dictionary for parameter indexing misses some keys' + assert 'Cholesky' in idx_param_sing and 'a1' in idx_param_sing, \ + 'The dictionary for parameter indexing misses some keys' assert 'Cholesky' in idx_param_fitU and 'a1' in idx_param_fitU, \ 'The dictionary for parameter indexing misses some keys' assert 'log_SNR2' in idx_param_fitV and 'c_space' in idx_param_fitV \ @@ -289,8 +320,8 @@ def test_gradient(): # Initial parameters are correct parameters with some perturbation param0_fitU = np.random.randn(n_l+n_V) * 0.1 param0_fitV = np.random.randn(n_V+1) * 0.1 - param0_sing = np.random.randn(n_l+2) * 0.1 - param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 + param0_sing = np.random.randn(n_l+1) * 0.1 + # param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 param0_sing[idx_param_sing['a1']] += np.mean(np.tan(rho1 * np.pi / 2)) param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 @@ -300,7 +331,7 @@ def test_gradient(): ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing) # We test the gradient to the Cholesky factor vec = np.zeros(np.size(param0_sing)) @@ -308,21 +339,21 @@ def test_gradient(): dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' # We test the gradient to log(sigma^2) - vec = np.zeros(np.size(param0_sing)) - vec[idx_param_sing['log_sigma2']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, - idx_param_sing)[0], - param0_sing, vec) - assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' + # vec = np.zeros(np.size(param0_sing)) + # vec[idx_param_sing['log_sigma2']] = 1 + # dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + # XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + # XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + # l_idx, n_C, n_T, n_V, n_run, n_base, + # idx_param_sing)[0], + # param0_sing, vec) + # assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' # We test the gradient to a1 vec = np.zeros(np.size(param0_sing)) @@ -330,79 +361,100 @@ def test_gradient(): dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - l_idx, n_C, n_T, n_V, n_run, + l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing)[0], param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt a1 is incorrect' # log likelihood and derivative of the fitU function. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitU(param0_fitU, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, \ - XTY, XTDY, XTFY, np.log(snr)*2, l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C) - - # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct - vec = np.zeros(np.size(param0_fitU)) - vec[idx_param_fitU['Cholesky'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ - YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], - param0_fitU, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect' + ll0, deriv0 = brsa._loglike_AR1_diagV_fitU(param0_fitU, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx,n_C,n_T,n_V,n_run,n_base,idx_param_fitU,n_C) + # We test the gradient wrt the reparametrization of AR(1) coefficient of noise. vec = np.zeros(np.size(param0_fitU)) vec[idx_param_fitU['a1'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ - YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], - param0_fitU, vec) + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitU, n_C)[0], param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt to AR(1) coefficient incorrect' + # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct + vec = np.zeros(np.size(param0_fitU)) + vec[idx_param_fitU['Cholesky'][0]] = 1 + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run,n_base, + idx_param_fitU, n_C)[0], param0_fitU, vec) + assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect' + # Test on a random direction vec = np.random.randn(np.size(param0_fitU)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\ - YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\ - l_idx,n_C,n_T,n_V,n_run,idx_param_fitU,n_C)[0], - param0_fitU, vec) + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitU, n_C)[0], param0_fitU, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU incorrect' # We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior. - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY = \ + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ brsa._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, - X0TY, X0TDY, X0TFY, L_full, rho1) + X0TY, X0TDY, X0TFY, + L_full, rho1, n_V, n_base) assert np.ndim(XTAX) == 3, 'Dimension of XTAX is wrong by _calc_sandwidge()' assert XTAY.shape == XTY.shape, 'Shape of XTAY is wrong by _calc_sandwidge()' assert YTAY.shape == YTY_diag.shape, 'Shape of YTAY is wrong by _calc_sandwidge()' assert np.ndim(X0TAX0) == 3, 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' assert np.ndim(XTAX0) == 3, 'Dimension of XTAX0 is wrong by _calc_sandwidge()' assert X0TAY.shape == X0TY.shape, 'Shape of X0TAX0 is wrong by _calc_sandwidge()' + assert np.all(np.isfinite(X0TAX0_i)), 'Inverse of X0TAX0 includes NaN or Inf' ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV[idx_param_fitV['log_SNR2']], - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,False,False) + l_idx,n_C,n_T,n_V,n_run,n_base, + idx_param_fitV,n_C,False,False) vec = np.zeros(np.size(param0_fitV[idx_param_fitV['log_SNR2']])) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, False, False)[0], + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, False, False)[0], param0_fitV[idx_param_fitV['log_SNR2']], vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' # We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx,n_C,n_T,n_V,n_run,idx_param_fitV,n_C,True,True, + l_idx,n_C,n_T,n_V,n_run,n_base, + idx_param_fitV,n_C,True,True, dist2,inten_diff2,100,100) vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV srt log(SNR2) incorrect for model with GP' @@ -410,9 +462,12 @@ def test_gradient(): # We test the graident wrt spatial length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_space']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt spatial length scale of GP incorrect' @@ -420,9 +475,12 @@ def test_gradient(): # We test the graident wrt intensity length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_inten']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt intensity length scale of GP incorrect' @@ -430,9 +488,12 @@ def test_gradient(): # We test the graident on a random direction vec = np.random.randn(np.size(param0_fitV)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, LTXTAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, + LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), - l_idx, n_C, n_T, n_V, n_run, idx_param_fitV, n_C, True, True, + l_idx, n_C, n_T, n_V, n_run, n_base, + idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV incorrect' From f1e432f2b4b952c192cbcb85569a60ac8968d8d5 Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 13 Oct 2016 00:13:58 -0400 Subject: [PATCH 14/30] attempt to solve conflict Changes to be committed: modified: brainiak/reprsimil/brsa.py modified: brainiak/utils/utils.py modified: examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb modified: tests/reprsimil/test_brsa.py modified: tests/utils/test_utils.py --- brainiak/reprsimil/brsa.py | 399 +++++++++++------- brainiak/utils/utils.py | 51 ++- ...tational_similarity_estimate_example.ipynb | 316 +++++++++----- tests/reprsimil/test_brsa.py | 119 +++--- tests/utils/test_utils.py | 14 +- 5 files changed, 558 insertions(+), 341 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 39b2559c1..23e41f8c0 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -63,7 +63,7 @@ class BRSA(BaseEstimator): will be provided as a quantification of neural representational similarity. .. math:: \textbf{Y = \textbf{X} \cdot \mbox{\boldmath{$\beta$}} - + \mbox{\boldmath{$\epsilon$}} + + \mbox{\boldmath{$\eta$}} .. math:: \mbox{\boldmath{$\beta$}}_i \sim \textbf{N}(0,(s_{i} \sigma_{i})^2 \textbf{U}) @@ -78,6 +78,26 @@ class BRSA(BaseEstimator): (e.g., calculating the similarity matrix of responses to each event), you might want to start with specifying a lower rank and use metrics such as AIC or BIC to decide the optimal rank. + auto_nuiance: boolean, default: True + In order to model spatial correlation between voxels that cannot + be accounted for by common response captured in the design matrix, + we assume that a set of time courses not related to the task + conditions are shared across voxels with unknown amplitudes. + One approach is for users to provide time series which they consider + as nuiance but exist in the noise (such as head motion). + The other way is to take the first n_nureg principal components + in the residual after one fitting of the Bayesian RSA model, and use + these components as the nuisance regressor. + If this flag is turned on, the nuiance regressor provided by the + user is used only in the first round of fitting. The PCs from + residuals will be used in the next round of fitting. + Note that nuiance regressor is not required from user. If it is + not provided, DC components for each run will be used as nuiance + regressor in the initial fitting. + n_nureg: int, default: 6 + Number of nuiance regressors to use in order to model signals + shared across voxels not captured by the design matrix. + This parameter will not be effective in the first round of fitting. GP_space: boolean, default: False Whether to impose a Gaussion Process (GP) prior on the log(pseudo-SNR). If true, the GP has a kernel defined over spatial coordinate. @@ -92,7 +112,7 @@ class BRSA(BaseEstimator): tol: tolerance parameter passed to the minimizer. verbose : boolean, default: False Verbose mode flag. - epsilon: a small number added to the diagonal element of the + eta: a small number added to the diagonal element of the covariance matrix in the Gaussian Process prior. This is to ensure that the matrix is invertible. space_smooth_range: the distance (in unit the same as what @@ -158,16 +178,18 @@ class BRSA(BaseEstimator): def __init__( self, n_iter=50, rank=None, GP_space=False, GP_inten=False, - tol=2e-3, verbose=False, epsilon=0.0001, - space_smooth_range=None, inten_smooth_range=None, + tol=2e-3, auto_nuiance=True, n_nureg=6, verbose=False, + eta=0.0001, space_smooth_range=None, inten_smooth_range=None, tau_range=10.0, init_iter=20, optimizer='BFGS', rand_seed=0): self.n_iter = n_iter self.rank = rank self.GP_space = GP_space self.GP_inten = GP_inten self.tol = tol + self.auto_nuiance = auto_nuiance + self.n_nureg = n_nureg self.verbose = verbose - self.epsilon = epsilon + self.eta = eta # This is a tiny ridge added to the Gaussian Process # covariance matrix template to gaurantee that it is invertible. # Mathematically it means we assume that this proportion of the @@ -185,7 +207,7 @@ def __init__( self.rand_seed = rand_seed return - def fit(self, X, design, scan_onsets=None, coords=None, + def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, inten=None): """Compute the Bayesian RSA @@ -200,16 +222,37 @@ def fit(self, X, design, scan_onsets=None, coords=None, This is the design matrix. It should only include the hypothetic response for task conditions. You do not need to include regressors for a DC component or motion parameters, unless with - a strong reason. + a strong reason. If you want to model DC component or head motion, + you should include them in nuiance regressors. + If you have multiple run, the design matrix + of all runs should be concatenated along the time dimension, + with one column across runs for each condition. + nuiance: optional, 2-D numpy array, + shape=[time_points, nuiance_factors] + The responses to these regressors will be marginalized out from + each voxel, which means they are considered, but won't be assumed + to share the same pseudo-SNR map with with the design matrix. + Therefore, the pseudo-SNR map will only reflect the + relative contribution of design matrix to each voxel. + You can provide time courses such as those for head motion + to this parameter. + Note that if auto_nuiance is set to True, this input + will only be used in the first round of fitting. The first + n_nureg principal components of residual (excluding the response + to the design matrix) will be used as the nuiance regressor + for the second round of fitting. + If auto_nuiance is set to False, the nuiance regressors supplied + by the users together with DC components will be used as + nuiance time series. scan_onsets: optional, an 1-D numpy array, shape=[runs,] - this specifies the indices of X which correspond to the onset + This specifies the indices of X which correspond to the onset of each scanning run. For example, if you have two experimental runs of the same subject, each with 100 TRs, then scan_onsets should be [0,100]. If you do not provide the argument, the program will assume all data are from the same run. - This only makes a difference for the inverse - of the temporal covariance matrix of noise. + The effect of them is to make the inverse matrix + of the temporal covariance matrix of noise block-diagonal. coords: optional, 2-D numpy array, shape=[voxels,3] This is the coordinate of each voxel, used for implementing Gaussian Process prior. @@ -253,6 +296,17 @@ def fit(self, X, design, scan_onsets=None, coords=None, assert self.rank is None or self.rank <= design.shape[1],\ 'Your design matrix has fewer columns than the rank you set' + # Check the nuiance regressors. + if nuiance is not None: + assert_all_finite(nuiance) + assert np.linalg.matrix_rank(nuiance) == nuiance.shape[1], \ + 'The nuiance regressor has rank smaller than the number of'\ + 'columns. Some columns can be explained by linear '\ + 'combination of other columns. Please check your nuiance' \ + 'regressors.' + assert np.size(nuiance, axis=0) == np.size(X, axis=0), \ + 'Nuiance regressor and data do not have the same '\ + ' number of time points.' # check scan_onsets validity assert scan_onsets is None or\ (np.max(scan_onsets) <= X.shape[0] and np.min(scan_onsets) >= 0),\ @@ -292,26 +346,32 @@ def fit(self, X, design, scan_onsets=None, coords=None, if not self.GP_space: # If GP_space is not requested, then the model is fitted # without imposing any Gaussian Process prior on log(SNR^2) - self.U_, self.L_, self.nSNR_, self.sigma_, self.rho_ = \ - self._fit_RSA_UV(X=design, Y=X, scan_onsets=scan_onsets) + self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ + self.sigma_, self.rho_ = \ + self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + scan_onsets=scan_onsets) elif not self.GP_inten: # If GP_space is requested, but GP_inten is not, a GP prior # based on spatial locations of voxels will be imposed. - self.U_, self.L_, self.nSNR_, self.sigma_, self.rho_,\ - self.lGPspace_, self.bGP_ = self._fit_RSA_UV( - X=design, Y=X, scan_onsets=scan_onsets, coords=coords) + self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ + self.sigma_, self.rho_, self.lGPspace_, self.bGP_ \ + = self._fit_RSA_UV( + X=design, Y=X, X0=nuiance, + scan_onsets=scan_onsets, coords=coords) else: # If both self.GP_space and self.GP_inten are True, # a GP prior based on both location and intensity is imposed. - self.U_, self.L_, self.nSNR_, self.sigma_, self.rho_, \ - self.lGPspace_, self.bGP_, self.lGPinten_ = \ - self._fit_RSA_UV(X=design, Y=X, scan_onsets=scan_onsets, + self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ + self.sigma_, self.rho_, self.lGPspace_, self.bGP_,\ + self.lGPinten_ = \ + self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + scan_onsets=scan_onsets, coords=coords, inten=inten) self.C_ = utils.cov2corr(self.U_) return self - # The following 2 functions below generate templates used + # The following 2 functions _D_gen and _F_gen generate templates used # for constructing inverse of covariance matrix of AR(1) noise # The inverse of covarian matrix is # (I - rho1 * D + rho1**2 * F) / sigma**2. D is a matrix where all the @@ -349,13 +409,15 @@ def _F_gen(self, TR): else: return np.empty([0, 0]) - def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): + def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): """Prepares different forms of products of design matrix X and data Y, or between themselves. These products are reused a lot during fitting. So we pre-calculate them. Because of the fact that these are reused, it is in principle possible to update the fitting as new data come in, by just incrementally adding the products of new data and their corresponding part of design matrix + no_DC means not inserting regressors for DC components into nuiance + regressor. It will only take effect if X0 is not None. """ if scan_onsets is None: # assume that all data are acquired within the same scan. @@ -408,15 +470,16 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None): ' columns in your design matrix are for ' ' conditions of interest.') if X0 is not None: - res0 = np.linalg.lstsq(X_base, X0) - if not np.any(np.isclose(res0[1], 0)): - # No columns in X0 can be explained by the - # baseline regressors. So we insert them. - X0 = np.insert(X0, 0, X_base, axis=1) - else: - logger.warning('Provided regressors for non-interesting ' - 'time series already include baseline. ' - 'No additional baseline is inserted.') + if not no_DC: + res0 = np.linalg.lstsq(X_base, X0) + if not np.any(np.isclose(res0[1], 0)): + # No columns in X0 can be explained by the + # baseline regressors. So we insert them. + X0 = np.concatenate(X_base, X0, axis=1) + else: + logger.warning('Provided regressors for non-interesting ' + 'time series already include baseline. ' + 'No additional baseline is inserted.') else: # If a set of regressors for non-interested signals is not # provided, then we simply include one baseline for each run. @@ -478,9 +541,9 @@ def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, # dimension: #baseline*space X0TAX0_i = np.linalg.solve(X0TAX0, np.identity(n_base)[None, :, :]) # dimension: space*#baseline*#baseline - XTAcorrX = XTAX.copy() + XTAcorrX = XTAX # dimension: space*feature*feature - XTAcorrY = XTAY.copy() + XTAcorrY = XTAY # dimension: feature*space for i_v in range(n_V): XTAcorrX[i_v, :, :] -= \ @@ -499,9 +562,37 @@ def _calc_sandwidge(self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, X0TAX0_i, X0TAY), axis=0) # dimension: space - return XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + return X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL + def _calc_LL(self, rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, SNR2, + n_V, n_T, n_run, rank, n_base): + # Calculate the log likelihood (excluding the GP prior of log(SNR)) + # for both _loglike_AR1_diagV_fitU and _loglike_AR1_diagV_fitV, + # in addition to a few other terms. + LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) + # dimension: space*rank*rank + LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) + # dimension: space*rank*rank + # LAMBDA is essentially the inverse covariance matrix of the + # posterior probability of alpha, which bears the relation with + # beta by beta = L * alpha. L is the Cholesky factor of the + # shared covariance matrix U. Refer to the explanation below + # Equation 5 in the NIPS paper. + + YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) + # dimension: space*rank + sigma2 = (YTAcorrY - np.sum(LTXTAcorrY * YTAcorrXL_LAMBDA.T, axis=0) + * SNR2) / (n_T - n_base) + # dimension: space + LL = - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5 \ + + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ + - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5 \ + - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ + - (n_T - n_base) * n_V * (1 + np.log(2 * np.pi)) * 0.5 + # Log likelihood + return LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 + def _calc_dist2_GP(self, coords=None, inten=None, GP_space=False, GP_inten=False): # calculate the square of difference between each voxel's location @@ -562,7 +653,7 @@ def _build_index_param(self, n_l, n_V, n_smooth): # each voxel) return idx_param_sing, idx_param_fitU, idx_param_fitV - def _fit_RSA_UV(self, X, Y, + def _fit_RSA_UV(self, X, Y, X0, scan_onsets=None, coords=None, inten=None): """ The major utility of fitting Bayesian RSA. Note that there is a naming change of variable. X in fit() @@ -612,10 +703,13 @@ def _fit_RSA_UV(self, X, Y, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets) + = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + X0=X0, no_DC=False) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and # gradient. + # DC component will be added to the nuiance regressors. + # In later steps, we do not need to add DC components again dist2, inten_diff2, space_smooth_range, inten_smooth_range,\ n_smooth = self._calc_dist2_GP( @@ -651,7 +745,7 @@ def _fit_RSA_UV(self, X, Y, # as the number of iteration. # Step 1 fitting, with a simplified model - current_vec_U_chlsk_l_AR1, current_a1, current_logSigma2 = \ + current_vec_U_chlsk_l, current_a1, current_logSigma2 = \ self._initial_fit_singpara( XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, @@ -662,18 +756,16 @@ def _fit_RSA_UV(self, X, Y, current_logSNR2 = -current_logSigma2 norm_factor = np.mean(current_logSNR2) current_logSNR2 = current_logSNR2 - norm_factor - # current_vec_U_chlsk_l_AR1 = current_vec_U_chlsk_l_AR1 \ - # * np.exp(norm_factor / 2.0) # Step 2 fitting, which only happens if # GP prior is requested if GP_space: - current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 \ + current_vec_U_chlsk_l, current_a1, current_logSNR2 \ = self._fit_diagV_noGP( XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank) @@ -701,32 +793,39 @@ def _fit_RSA_UV(self, X, Y, # many voxels have close to equal intensities, # which might render 5 percential to 0. - # Step 3 fitting. + # Step 3 fitting. GP prior is imposed if requested. + # In this step, unless auto_nuiance is set to False, X0 + # will be re-estimated from the residuals after each step + # of fitting. logger.debug('indexing:{}'.format(idx_param_fitV)) logger.debug('initial GP parameters:{}'.format(current_GP)) - current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2,\ - current_GP = self._fit_diagV_GP( - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, current_logSNR2,\ + current_GP, X0 = self._fit_diagV_GP( + X, Y, scan_onsets, X0, + current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range) - logger.debug('final GP parameters:{}'.format(current_GP)) estU_chlsk_l_AR1_UV = np.zeros([n_C, rank]) - estU_chlsk_l_AR1_UV[l_idx] = current_vec_U_chlsk_l_AR1 + estU_chlsk_l_AR1_UV[l_idx] = current_vec_U_chlsk_l est_cov_AR1_UV = np.dot(estU_chlsk_l_AR1_UV, estU_chlsk_l_AR1_UV.T) est_rho1_AR1_UV = 2 / np.pi * np.arctan(current_a1) est_SNR_AR1_UV = np.exp(current_logSNR2 / 2.0) - # Calculating est_sigma_AR1_UV - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + # Calculating est_sigma_AR1_UV, est_sigma_AR1_UV, + # est_beta_AR1_UV and est_beta0_AR1_UV + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_run, n_base \ + = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + X0=X0, no_DC=True) + + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL\ = self._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, @@ -734,20 +833,21 @@ def _fit_RSA_UV(self, X, Y, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, estU_chlsk_l_AR1_UV, est_rho1_AR1_UV, n_V, n_base) - LAMBDA_i = LTXTAcorrXL * est_SNR_AR1_UV[:, None, None]**2 \ - + np.eye(rank) - # dimension: space*rank*rank - LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) - # dimension: space*rank*rank - YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) - # dimension: space*rank - est_sigma_AR1_UV = ((YTAcorrY - np.sum(LTXTAcorrY - * YTAcorrXL_LAMBDA.T, axis=0) - * est_SNR_AR1_UV**2) / (n_T - n_base)) ** 0.5 + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(est_rho1_AR1_UV, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, est_SNR_AR1_UV**2, + n_V, n_T, n_run, rank, n_base) + est_sigma_AR1_UV = sigma2**0.5 + est_beta_AR1_UV = est_sigma_AR1_UV * est_SNR_AR1_UV**2 \ + * np.dot(estU_chlsk_l_AR1_UV, YTAcorrXL_LAMBDA.T) + est_beta0_AR1_UV = np.einsum( + 'ijk,ki->ji', X0TAX0_i, + (X0TAY - np.einsum('ikj,ki->ji', XTAX0, est_beta_AR1_UV))) t_finish = time.time() logger.info( 'total time of fitting: {} seconds'.format(t_finish - t_start)) + logger.debug('final GP parameters:{}'.format(current_GP)) if GP_space: est_space_smooth_r = np.exp(current_GP[0] / 2.0) if GP_inten: @@ -755,25 +855,28 @@ def _fit_RSA_UV(self, X, Y, K_major = np.exp(- (dist2 / est_space_smooth_r**2 + inten_diff2 / est_intensity_kernel_r**2) / 2.0) - K = K_major + np.diag(np.ones(n_V) * self.epsilon) + K = K_major + np.diag(np.ones(n_V) * self.eta) est_std_log_SNR = (np.dot(current_logSNR2, np.dot( np.linalg.inv(K), current_logSNR2)) / n_V / 4)**0.5 # divided by 4 because we used # log(SNR^2) instead of log(SNR) return est_cov_AR1_UV, estU_chlsk_l_AR1_UV, est_SNR_AR1_UV, \ - est_sigma_AR1_UV, est_rho1_AR1_UV, est_space_smooth_r, \ + est_beta_AR1_UV, est_beta0_AR1_UV, est_sigma_AR1_UV, \ + est_rho1_AR1_UV, est_space_smooth_r, \ est_std_log_SNR, est_intensity_kernel_r # When GP_inten is True, the following lines won't be reached else: K_major = np.exp(- dist2 / est_space_smooth_r**2 / 2.0) - K = K_major + np.diag(np.ones(n_V) * self.epsilon) + K = K_major + np.diag(np.ones(n_V) * self.eta) est_std_log_SNR = (np.dot(current_logSNR2, np.dot( np.linalg.inv(K), current_logSNR2)) / n_V / 4)**0.5 return est_cov_AR1_UV, estU_chlsk_l_AR1_UV, est_SNR_AR1_UV, \ + est_beta_AR1_UV, est_beta0_AR1_UV, \ est_sigma_AR1_UV, est_rho1_AR1_UV, est_space_smooth_r, \ est_std_log_SNR else: return est_cov_AR1_UV, estU_chlsk_l_AR1_UV, est_SNR_AR1_UV, \ + est_beta_AR1_UV, est_beta0_AR1_UV, \ est_sigma_AR1_UV, est_rho1_AR1_UV def _initial_fit_singpara(self, XTX, XTDX, XTFX, @@ -800,7 +903,7 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, # (1) start from the point estimation of covariance # cov_point_est = np.cov(beta_hat) - # current_vec_U_chlsk_l_AR1 = \ + # current_vec_U_chlsk_l = \ # np.linalg.cholesky(cov_point_est + \ # np.eye(n_C) * 1e-6)[l_idx] @@ -811,11 +914,11 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, # (2) start from identity matrix - # current_vec_U_chlsk_l_AR1 = np.eye(n_C)[l_idx] + # current_vec_U_chlsk_l = np.eye(n_C)[l_idx] # (3) random initialization - current_vec_U_chlsk_l_AR1 = np.random.randn(n_l) + current_vec_U_chlsk_l = np.random.randn(n_l) # vectorized version of L, Cholesky factor of U, the shared # covariance matrix of betas across voxels. @@ -831,9 +934,8 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, for v in idx_param_sing.values())) # Initial parameter # Then we fill each part of the original guess of parameters - param0[idx_param_sing['Cholesky']] = current_vec_U_chlsk_l_AR1 + param0[idx_param_sing['Cholesky']] = current_vec_U_chlsk_l param0[idx_param_sing['a1']] = np.median(np.tan(rho1 * np.pi / 2)) - # param0[idx_param_sing['log_sigma2']] = np.median(log_sigma2) # Fit it. res = scipy.optimize.minimize( @@ -845,26 +947,26 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, idx_param_sing, rank), method=self.optimizer, jac=True, tol=self.tol, options={'disp': self.verbose, 'maxiter': 100}) - current_vec_U_chlsk_l_AR1 = res.x[idx_param_sing['Cholesky']] + current_vec_U_chlsk_l = res.x[idx_param_sing['Cholesky']] current_a1 = res.x[idx_param_sing['a1']] * np.ones(n_V) # log(sigma^2) assuming the data include no signal is returned, # as a starting point for the iteration in the next step. # Although it should overestimate the variance, # setting it this way might allow it to track log(sigma^2) # more closely for each voxel. - return current_vec_U_chlsk_l_AR1, current_a1, log_sigma2 + return current_vec_U_chlsk_l, current_a1, log_sigma2 def _fit_diagV_noGP( self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank): """ (optional) second step of fitting, full model but without - GP prior on log(SNR). This is only used when GP is - requested. + GP prior on log(SNR). This step is only done if GP prior + is requested. """ init_iter = self.init_iter logger.info('second fitting without GP prior' @@ -877,7 +979,7 @@ def _fit_diagV_noGP( # We cannot use the same logic as the line above because # idx_param_fitV also includes entries for GP parameters. param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1.copy() + current_vec_U_chlsk_l.copy() param0_fitU[idx_param_fitU['a1']] = current_a1.copy() param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() @@ -886,9 +988,14 @@ def _fit_diagV_noGP( tol = self.tol * 5 for it in range(0, init_iter): # fit V, reflected in the log(SNR^2) of each voxel + # XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + # XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + # X0TY, X0TDY, X0TFY, X0, n_run, n_base \ + # = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + # X0=X0) rho1 = np.arctan(current_a1) * 2 / np.pi - L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + L[l_idx] = current_vec_U_chlsk_l + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, \ LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, @@ -900,10 +1007,10 @@ def _fit_diagV_noGP( L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, - args=(XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + args=(X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, - current_vec_U_chlsk_l_AR1, + current_vec_U_chlsk_l, current_a1, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitV, rank, False, False), @@ -933,7 +1040,7 @@ def _fit_diagV_noGP( # fit U, the covariance matrix, together with AR(1) param param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1 + current_vec_U_chlsk_l param0_fitU[idx_param_fitU['a1']] = current_a1 res_fitU = scipy.optimize.minimize( self._loglike_AR1_diagV_fitU, param0_fitU, @@ -945,7 +1052,7 @@ def _fit_diagV_noGP( method=self.optimizer, jac=True, tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 3}) - current_vec_U_chlsk_l_AR1 = \ + current_vec_U_chlsk_l = \ res_fitU.x[idx_param_fitU['Cholesky']] current_a1 = res_fitU.x[idx_param_fitU['a1']] norm_fitUchange = np.linalg.norm(res_fitU.x - param0_fitU) @@ -957,19 +1064,17 @@ def _fit_diagV_noGP( and norm_fitUchange / np.sqrt(param0_fitU.size) \ < tol: break - return current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2 + return current_vec_U_chlsk_l, current_a1, current_logSNR2 def _fit_diagV_GP( - self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_vec_U_chlsk_l_AR1, + self, X, Y, scan_onsets, X0, + current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range): - """ Last step of fitting. If GP is not requested, it will still - fit. + """ Last step of fitting. If GP is not requested, this step will + still be done, just without GP prior on log(SNR). """ tol = self.tol n_iter = self.n_iter @@ -984,23 +1089,24 @@ def _fit_diagV_GP( # We cannot use the same logic as the line above because # idx_param_fitV also includes entries for GP parameters. param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1.copy() + current_vec_U_chlsk_l.copy() param0_fitU[idx_param_fitU['a1']] = current_a1.copy() param0_fitV[idx_param_fitV['log_SNR2']] = \ current_logSNR2[:-1].copy() L = np.zeros((n_C, rank)) + L[l_idx] = current_vec_U_chlsk_l if self.GP_space: param0_fitV[idx_param_fitV['c_both']] = current_GP.copy() - # param0_fitV[idx_param_fitV['c_space']] = \ - # current_GP[0] - # if self.GP_inten: - # param0_fitV[idx_param_fitV['c_inten']] = \ - # current_GP[1] + for it in range(0, n_iter): + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_run, n_base \ + = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, + X0=X0, no_DC=True) # fit V rho1 = np.arctan(current_a1) * 2 / np.pi - L[l_idx] = current_vec_U_chlsk_l_AR1 - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, \ LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, @@ -1012,17 +1118,17 @@ def _fit_diagV_GP( L, rho1, n_V, n_base) res_fitV = scipy.optimize.minimize( self._loglike_AR1_diagV_fitV, param0_fitV, args=( - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, + X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, - current_vec_U_chlsk_l_AR1, current_a1, + current_vec_U_chlsk_l, current_a1, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitV, rank, GP_space, GP_inten, dist2, inten_diff2, space_smooth_range, inten_smooth_range), method=self.optimizer, jac=True, - tol=tol, # 10**(-2 - 2 / n_iter * (it + 1)), - options={'xtol': tol, # 10**(-3 - 3 / n_iter * (it + 1)), + tol=tol, + options={'xtol': tol, 'disp': self.verbose, 'maxiter': 6}) current_logSNR2[0:n_V - 1] = \ @@ -1042,7 +1148,7 @@ def _fit_diagV_GP( # fit U param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l_AR1 + current_vec_U_chlsk_l param0_fitU[idx_param_fitU['a1']] = current_a1 res_fitU = scipy.optimize.minimize( @@ -1056,17 +1162,30 @@ def _fit_diagV_GP( tol=tol, options={'xtol': tol, 'disp': self.verbose, 'maxiter': 6}) - current_vec_U_chlsk_l_AR1 = \ + current_vec_U_chlsk_l = \ res_fitU.x[idx_param_fitU['Cholesky']] current_a1 = res_fitU.x[idx_param_fitU['a1']] - + L[l_idx] = current_vec_U_chlsk_l fitUchange = res_fitU.x - param0_fitU norm_fitUchange = np.linalg.norm(fitUchange) logger.debug('norm of parameter change after fitting U: ' '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() - # Debugging purpose. But it exceeds complexity limit + current_SNR2 = np.exp(current_logSNR2) + + # Re-estimating X0 from residuals + if self.auto_nuiance: + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, current_sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, current_SNR2, + n_V, n_T, n_run, rank, n_base) + betas = current_sigma2**0.5 * current_SNR2 \ + * np.dot(L, YTAcorrXL_LAMBDA.T) + residuals = Y - np.dot(X, betas) + u, s, v = np.linalg.svd(residuals) + X0 = u[:, :self.n_nureg] + if GP_space: logger.debug('current GP[0]: {}'.format(current_GP[0])) logger.debug('gradient for GP[0]: {}'.format( @@ -1079,8 +1198,8 @@ def _fit_diagV_GP( np.max(np.abs(fitUchange)) < tol: break - return current_vec_U_chlsk_l_AR1, current_a1, current_logSNR2,\ - current_GP + return current_vec_U_chlsk_l, current_a1, current_logSNR2,\ + current_GP, X0 # We fit two parts of the parameters iteratively. # The following are the corresponding negative log likelihood functions. @@ -1132,7 +1251,7 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # each element of SNR2 is the ratio of the diagonal element on V # to the variance of the fresh noise in that voxel - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, \ LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ self._calc_sandwidge(XTY, XTDY, XTFY, @@ -1142,35 +1261,16 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, L, rho1, n_V, n_base) # Only starting from this point, SNR2 is involved - LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) - # dimension: space*rank*rank - LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) - # dimension: space*rank*rank - # LAMBDA is essentially the inverse covariance matrix of the - # posterior probability of alpha, which bears the relation with - # beta by beta = L * alpha, and L is the Cholesky factor of the - # shared covariance matrix U. refer to the explanation below - # Equation 5 in the NIPS paper. - - # LAMBDA_LTXTAcorrY = np.einsum('ijk,ki->ji', LAMBDA_i, LTXTAcorrY) - YTAcorrXL_LAMBDA = np.einsum('ji,ijk->ik', LTXTAcorrY, LAMBDA) - # dimension: space*rank - # # dimension: feature*space - sigma2 = (YTAcorrY - np.sum(LTXTAcorrY * YTAcorrXL_LAMBDA.T, axis=0) - * SNR2) / (n_T - n_base) - - LL = - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5 \ - + np.sum(np.log(1 - rho1**2)) * n_run * 0.5 \ - - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5 \ - - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5 \ - - (n_T - n_base) * n_V * (1 + np.log(2 * np.pi)) * 0.5 + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, + SNR2, n_V, n_T, n_run, rank, n_base) if not np.isfinite(LL): - print('NaN detected!') - print(sigma2) - print(YTAcorrY) - print(LTXTAcorrY) - print(YTAcorrXL_LAMBDA) - print(SNR2) + logger.debug('NaN detected!') + logger.debug(sigma2) + logger.debug(YTAcorrY) + logger.debug(LTXTAcorrY) + logger.debug(YTAcorrXL_LAMBDA) + logger.debug(SNR2) YTAcorrXL_LAMBDA_LT = np.dot(YTAcorrXL_LAMBDA, L.T) # dimension: space*feature (feature can be larger than rank) @@ -1240,13 +1340,13 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, dXTAcorrX_drho1_ele), YTAcorrXL_LAMBDA_LT[i_v, :])) - deriv = np.zeros(np.size(param)) + deriv = np.empty(np.size(param)) deriv[idx_param_fitU['Cholesky']] = deriv_L[l_idx] deriv[idx_param_fitU['a1']] = deriv_a1 return -LL, -deriv - def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, + def _loglike_AR1_diagV_fitV(self, param, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, @@ -1303,24 +1403,9 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # If requested, a GP prior is imposed on log(SNR). rho1 = 2.0 / np.pi * np.arctan(a1) # AR(1) coefficient, dimension: space - LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) - - # dimension: space*rank*rank - LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) - # dimension: space*rank*rank - YTAcorrXL_LAMBDA = np.einsum('ijk,ki->ij', LAMBDA, LTXTAcorrY) - # dimension: space*rank - sigma2 = (YTAcorrY - - SNR2 * np.sum(YTAcorrXL_LAMBDA - * LTXTAcorrY.T, axis=1)) / (n_T - n_base) - # dimension: space - - LL = - (n_T - n_base) * np.log(2 * np.pi) * 0.5\ - - np.sum(np.log(sigma2)) * (n_T - n_base) * 0.5\ - + np.sum(np.log(1 - rho1**2)) * n_run * 0.5\ - - np.sum(np.log(np.linalg.det(X0TAX0))) * 0.5\ - - np.sum(np.log(np.linalg.det(LAMBDA_i))) * 0.5\ - - (n_T - n_base) * n_V * 0.5 + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, + SNR2, n_V, n_T, n_run, rank, n_base) # Log likelihood of data given parameters, without the GP prior. deriv_log_SNR2 = (-rank + np.trace(LAMBDA, axis1=1, axis2=2)) * 0.5\ + YTAcorrY / (sigma2 * 2.0) - (n_T - n_base) * 0.5 \ @@ -1356,7 +1441,7 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # The kernel defined over the spatial coordinates of voxels. # This is a template: the diagonal values are all 1, meaning # the variance of log(SNR) has not been multiplied - K_tilde = K_major + np.diag(np.ones(n_V) * self.epsilon) + K_tilde = K_major + np.diag(np.ones(n_V) * self.eta) # We add a small number to the diagonal to make sure the matrix # is invertible. # Note that the K_tilder here is still template: @@ -1435,7 +1520,7 @@ def _loglike_AR1_diagV_fitV(self, param, XTAX, XTAY, YTAY, # the magnitude of log(SNR). deriv_log_SNR2 += - log_SNR2 / self.tau_range**2 / 4.0 - deriv = np.zeros(np.size(param)) + deriv = np.empty(np.size(param)) deriv[idx_param_fitV['log_SNR2']] = \ deriv_log_SNR2[0:n_V - 1] - deriv_log_SNR2[n_V - 1] if GP_space: @@ -1544,7 +1629,7 @@ def _loglike_AR1_singpara(self, param, XTX, XTDX, XTFX, YTY_diag, - 0.5 * np.sum(np.dot(dXTAcorrX_drho1, L_LAMBDA_LTXTAcorrY) * L_LAMBDA_LTXTAcorrY) / sigma2) - deriv = np.zeros(np.size(param)) + deriv = np.empty(np.size(param)) deriv[idx_param_sing['Cholesky']] = deriv_L[l_idx] deriv[idx_param_sing['a1']] = deriv_a1 diff --git a/brainiak/utils/utils.py b/brainiak/utils/utils.py index 0fbddb48c..a4e86d8e2 100644 --- a/brainiak/utils/utils.py +++ b/brainiak/utils/utils.py @@ -203,20 +203,25 @@ class ReadDesign: fname: string, the address of the file to read. include_orth: Boollean, whether to include "orthogonal" regressors in - the design matrix which are usually head motion parameters. All - the columns of design matrix are still going to be read in, but - the attribute cols_used will reflect whether these orthogonal + the nuisance regressors which are usually head motion parameters. + All the columns of design matrix are still going to be read in, + but the attribute cols_used will reflect whether these orthogonal regressors are to be included for furhter analysis. + Note that these are not entered into design_task attribute which + include only regressors related to task conditions. include_pols: Boollean, whether to include polynomial regressors in - the design matrix which are used to capture slow drift of signals. - This will be reflected in the indices in the attribute cols_used. + the nuisance regressors which are used to capture slow drift of + signals. Attributes ---------- design: 2d array. The design matrix read in from the csv file. + design_task: 2d array. The part of design matrix corresponding to + task conditions. + n_col: number of total columns in the design matrix. column_types: 1d array. the types of each column in the design matrix. @@ -233,7 +238,7 @@ class ReadDesign: StimLabels: list. The names of each column in the design matrix. """ - def __init__(self, fname=None, include_orth=False, include_pols=False): + def __init__(self, fname=None, include_orth=True, include_pols=True): if fname is None: # fname is the name of the file to read in the design matrix self.design = np.zeros([0, 0]) @@ -253,18 +258,32 @@ def __init__(self, fname=None, include_orth=False, include_pols=False): self.include_orth = include_orth self.include_pols = include_pols - self.cols_used = np.where(self.column_types == 1)[0] + # The two flags above dictates whether columns corresponding to + # baseline drift modeled by polynomial functions of time and + # columns corresponding to other orthogonal signals (usually motion) + # are included in nuisance regressors. + self.cols_task = np.where(self.column_types == 1)[0] + self.design_task = self.design[:, self.cols_task] + if np.ndim(self.design_task) == 1: + self.design_task = self.design_task[:, None] + # part of the design matrix related to task conditions. + self.n_TR = np.size(self.design_task, axis=0) + self.cols_nuisance = np.array([]) if self.include_orth: - self.cols_used = np.sort( - np.append(self.cols_used, np.where(self.column_types == 0)[0])) + self.cols_nuisance = np.int0( + np.sort(np.append(self.cols_nuisance, + np.where(self.column_types == 0)[0]))) if self.include_pols: - self.cols_used = np.sort(np.append( - self.cols_used, np.where(self.column_types == -1)[0])) - self.design_used = self.design[:, self.cols_used] - if not self.include_pols: - # baseline is not included, then we add a column of all 1's - self.design_used = np.insert(self.design_used, 0, 1, axis=1) - self.n_TR = np.size(self.design_used, axis=0) + self.cols_nuisance = np.int0( + np.sort(np.append(self.cols_nuisance, + np.where(self.column_types == -1)[0]))) + if np.size(self.cols_nuisance) > 0: + self.reg_nuisance = self.design[:, self.cols_nuisance] + if np.ndim(self.reg_nuisance) == 1: + self.reg_nuisance = self.reg_nuisance[:, None] + else: + self.reg_nuisance = None + # Nuisance regressors for motion, baseline, etc. def read_afni(self, fname): # Read design file written by AFNI diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 187727706..e78329a4f 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -1,12 +1,10 @@ { "cells": [ { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "collapsed": false }, - "outputs": [], "source": [ "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset." ] @@ -54,15 +52,17 @@ }, "outputs": [], "source": [ - "logging.basicConfig(level=logging.DEBUG, filename='brsa_example.log',\n", - " format='%(relativeCreated)6d %(threadName)s %(message)s')" + "logging.basicConfig(\n", + " level=logging.DEBUG,\n", + " filename='brsa_example.log',\n", + " format='%(relativeCreated)6d %(threadName)s %(message)s')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# (1) We want to simulate some data in which each voxel respond to different task conditions differently, but following a common covariance structure" + "# We want to simulate some data in which each voxel responds to different task conditions differently, but following a common covariance structure" ] }, { @@ -93,27 +93,33 @@ "design = utils.ReadDesign(fname=\"example_design.1D\")\n", "\n", "n_run = 2\n", - "design.design_used = np.tile(design.design_used[:,1:17],[n_run,1])\n", "design.n_TR = design.n_TR * n_run\n", - "\n", - "\n", - "fig = plt.figure(num=None, figsize=(12, 3), dpi=150, facecolor='w', edgecolor='k')\n", - "\n", - "plt.plot(design.design_used)\n", - "plt.ylim([-0.2,0.4])\n", - "plt.title('hypothetic fMRI response time courses of all conditions in addition to a DC component\\n'\n", + "design.design_task = np.tile(design.design_task[:,:-1],\n", + " [n_run, 1])\n", + "# The last \"condition\" in design matrix\n", + "# codes for trials subjects made and error.\n", + "# We ignore it here.\n", + "\n", + "\n", + "fig = plt.figure(num=None, figsize=(12, 3),\n", + " dpi=150, facecolor='w', edgecolor='k')\n", + "plt.plot(design.design_task)\n", + "plt.ylim([-0.2, 0.4])\n", + "plt.title('hypothetic fMRI response time courses '\n", + " 'of all conditions in addition to a DC component\\n'\n", " '(design matrix)')\n", "plt.xlabel('time')\n", "plt.show()\n", "\n", - "n_C = np.size(design.design_used,axis=1) \n", + "n_C = np.size(design.design_task, axis=1)\n", "# The total number of conditions.\n", - "ROI_edge = 25\n", + "ROI_edge = 20\n", "# We simulate \"ROI\" of a square shape\n", "n_V = ROI_edge**2\n", "# The total number of simulated voxels\n", "n_T = design.n_TR\n", - "# The total number of time points, after concatenating all fMRI runs\n" + "# The total number of time points,\n", + "# after concatenating all fMRI runs\n" ] }, { @@ -121,7 +127,7 @@ "metadata": {}, "source": [ "## simulate data: noise + signal\n", - "### First, we start with noise" + "### First, we start with noise, which is Gaussian Process in space and AR(1) in time" ] }, { @@ -134,7 +140,8 @@ "source": [ "noise_bot = 0.5\n", "noise_top = 1.5\n", - "noise_level = np.random.rand(n_V)*(noise_top-noise_bot)+noise_bot\n", + "noise_level = np.random.rand(n_V) * \\\n", + " (noise_top - noise_bot) + noise_bot\n", "# The standard deviation of the noise is in the range of [noise_bot, noise_top]\n", "# In fact, we simulate autocorrelated noise with AR(1) model. So the noise_level reflects\n", "# the independent additive noise at each time point (the \"fresh\" noise)\n", @@ -142,18 +149,44 @@ "# AR(1) coefficient\n", "rho1_top = 0.8\n", "rho1_bot = -0.2\n", - "rho1 = np.random.rand(n_V)*(rho1_top-rho1_bot)+rho1_bot\n", + "rho1 = np.random.rand(n_V) \\\n", + " * (rho1_top - rho1_bot) + rho1_bot\n", + "\n", "\n", + "noise_smooth_width = 10.0\n", + "coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", + "coords_flat = np.reshape(coords,[3, n_V]).T\n", + "dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", "\n", "# generating noise\n", - "noise = np.zeros([n_T,n_V])\n", - "noise[0,:] = np.random.randn(n_V) * noise_level / np.sqrt(1-rho1**2)\n", - "for i_t in range(1,n_T):\n", - " noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", + "K_noise = noise_level[:, np.newaxis] \\\n", + " * (np.exp(-dist2 / noise_smooth_width**2 / 2.0) \\\n", + " + np.eye(n_V) * 0.1) * noise_level\n", + "print(np.shape(K_noise))\n", + "plt.pcolor(K_noise)\n", + "plt.colorbar()\n", + "plt.xlim([0, ROI_edge * ROI_edge])\n", + "plt.ylim([0, ROI_edge * ROI_edge])\n", + "plt.title('Spatial covariance matrix of noise')\n", + "plt.show()\n", + "L_noise = np.linalg.cholesky(K_noise)\n", + "noise = np.zeros([n_T, n_V])\n", + "noise[0, :] = np.dot(L_noise, np.random.randn(n_V))\\\n", + " / np.sqrt(1 - rho1**2)\n", + "for i_t in range(1, n_T):\n", + " noise[i_t, :] = noise[i_t - 1, :] * rho1 \\\n", + " + np.dot(L_noise,np.random.randn(n_V))\n", + "\n", + "\n", + "# noise = np.zeros([n_T,n_V])\n", + "# noise[0,:] = np.random.randn(n_V) * noise_level / np.sqrt(1-rho1**2)\n", + "# for i_t in range(1,n_T):\n", + "# noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", "# Here, we assume noise is independent between voxels\n", "noise = noise + np.random.randn(n_V)\n", - "fig = plt.figure(num=None, figsize=(12, 2), dpi=150, facecolor='w', edgecolor='k')\n", - "plt.plot(noise[:,0])\n", + "fig = plt.figure(num=None, figsize=(12, 2), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", + "plt.plot(noise[:, 0])\n", "plt.title('noise in an example voxel')\n", "plt.show()" ] @@ -162,7 +195,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Then, we simulate signals, assuming the magnitude of response to each condition follows a common covariance matrix\n", + "### Then, we simulate signals, assuming the magnitude of response to each condition follows a common covariance matrix. \n", "#### Our model allows to impose a Gaussian Process prior on the log(SNR) of each voxels. \n", "What this means is that SNR turn to be smooth and local, but betas (response amplitudes of each voxel to each condition) are not necessarily correlated in space. Intuitively, this is based on the assumption that voxels coding for related aspects of a task turn to be clustered (instead of isolated)\n", "\n", @@ -177,7 +210,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "##### Note: the following code won't work if you just installed Brainiak. It serves as an example for you to retrieve coordinates of voxels in an ROI. You can use the ROI_coords for the argument coords in BRSA.fit()" + "##### Note: the following code won't work if you just installed Brainiak and try this demo because ROI.nii does not exist. It just serves as an example for you to retrieve coordinates of voxels in an ROI. You can use the ROI_coords for the argument coords in BRSA.fit()" ] }, { @@ -192,10 +225,11 @@ "# ROI = nibabel.load('ROI.nii')\n", "# I,J,K = ROI.shape \n", "# all_coords = np.zeros((I, J, K, 3)) \n", - "# all_coords[...,0] = np.arange(I)[:,np.newaxis,np.newaxis] \n", - "# all_coords[...,1] = np.arange(J)[np.newaxis,:,np.newaxis] \n", - "# all_coords[...,2] = np.arange(K)[np.newaxis,np.newaxis,:] \n", - "# ROI_coords = nibabel.affines.apply_affine(ROI.affine, all_coords[ROI.get_data().astype(bool)])\n" + "# all_coords[...,0] = np.arange(I)[:, np.newaxis, np.newaxis] \n", + "# all_coords[...,1] = np.arange(J)[np.newaxis, :, np.newaxis] \n", + "# all_coords[...,2] = np.arange(K)[np.newaxis, np.newaxis, :] \n", + "# ROI_coords = nibabel.affines.apply_affine(\n", + "# ROI.affine, all_coords[ROI.get_data().astype(bool)])\n" ] }, { @@ -214,29 +248,29 @@ "outputs": [], "source": [ "# ideal covariance matrix\n", - "ideal_cov = np.zeros([n_C,n_C])\n", - "ideal_cov = np.eye(n_C)*0.6\n", - "ideal_cov[8:12,8:12] = 0.8\n", - "for cond in range(8,12):\n", + "ideal_cov = np.zeros([n_C, n_C])\n", + "ideal_cov = np.eye(n_C) * 0.6\n", + "ideal_cov[8:12, 8:12] = 0.8\n", + "for cond in range(8, 12):\n", " ideal_cov[cond,cond] = 1\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_cov)\n", "plt.colorbar()\n", - "plt.xlim([0,16])\n", - "plt.ylim([0,16])\n", + "plt.xlim([0, 16])\n", + "plt.ylim([0, 16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal covariance matrix')\n", "plt.show()\n", "\n", "std_diag = np.diag(ideal_cov)**0.5\n", - "ideal_corr = ideal_cov / std_diag / std_diag[:,None]\n", + "ideal_corr = ideal_cov / std_diag / std_diag[:, None]\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(ideal_corr)\n", "plt.colorbar()\n", - "plt.xlim([0,16])\n", - "plt.ylim([0,16])\n", + "plt.xlim([0, 16])\n", + "plt.ylim([0, 16])\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('ideal correlation matrix')\n", @@ -247,7 +281,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### In the following, pseudo-SNR is generated from a Gaussian process defined on a \"linear\" ROI, just for simplicity of code" + "#### In the following, pseudo-SNR is generated from a Gaussian Process defined on a \"square\" ROI, just for simplicity of code" ] }, { @@ -258,16 +292,15 @@ }, "outputs": [], "source": [ - "\n", - "\n", "L_full = np.linalg.cholesky(ideal_cov) \n", "\n", "# generating signal\n", "snr_level = 0.6\n", - "# Notice that accurately speaking this is not snr. the magnitude of signal depends\n", - "# not only on beta but also on x. (noise_level*snr_level)**2 is the factor multiplied\n", - "# with ideal_cov to form the covariance matrix from which the response amplitudes (beta)\n", - "# of a voxel are drawn from.\n", + "# Notice that accurately speaking this is not SNR.\n", + "# The magnitude of signal depends not only on beta but also on x.\n", + "# (noise_level*snr_level)**2 is the factor multiplied\n", + "# with ideal_cov to form the covariance matrix from which\n", + "# the response amplitudes (beta) of a voxel are drawn from.\n", "\n", "tau = 0.8\n", "# magnitude of Gaussian Process from which the log(SNR) is drawn\n", @@ -280,12 +313,13 @@ "# then the smoothness has much small dependency on the intensity.\n", "\n", "\n", - "coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", - "coords_flat = np.reshape(coords,[3, n_V]).T\n", - "dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", + "# coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", + "# coords_flat = np.reshape(coords,[3, n_V]).T\n", + "# dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", "\n", "inten = np.random.rand(n_V) * 20.0\n", - "# For simplicity, we just assume that the intensity of all voxels are uniform distributed between 0 and 20\n", + "# For simplicity, we just assume that the intensity\n", + "# of all voxels are uniform distributed between 0 and 20\n", "# parameters of Gaussian process to generate pseuso SNR\n", "# For curious user, you can also try the following commond\n", "# to see what an example snr map might look like if the intensity\n", @@ -294,34 +328,39 @@ "# inten = coords_flat[:,0] * 2\n", "\n", "\n", - "inten_tile = np.tile(inten,[n_V,1])\n", - "inten_diff2 = (inten_tile-inten_tile.T)**2\n", + "inten_tile = np.tile(inten, [n_V, 1])\n", + "inten_diff2 = (inten_tile - inten_tile.T)**2\n", "\n", - "K = np.exp(-dist2/smooth_width**2/2.0 -inten_diff2/inten_kernel**2/2.0) * tau**2 \\\n", - " + np.eye(n_V)*tau**2*0.001\n", - "# A tiny amount is added to the diagonal of the GP covariance matrix to make sure it can be inverted\n", + "K = np.exp(-dist2 / smooth_width**2 / 2.0 \n", + " - inten_diff2 / inten_kernel**2 / 2.0) * tau**2 \\\n", + " + np.eye(n_V) * tau**2 * 0.001\n", + "# A tiny amount is added to the diagonal of\n", + "# the GP covariance matrix to make sure it can be inverted\n", "L = np.linalg.cholesky(K)\n", - "snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level\n", - "sqrt_v = noise_level*snr\n", - "betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v\n", - "signal = np.dot(design.design_used,betas_simulated)\n", + "snr = np.exp(np.dot(L, np.random.randn(n_V))) * snr_level\n", + "sqrt_v = noise_level * snr\n", + "betas_simulated = np.dot(L_full, np.random.randn(n_C, n_V)) * sqrt_v\n", + "signal = np.dot(design.design_task, betas_simulated)\n", "\n", "\n", "Y = signal + noise \n", "# The data to be fed to the program.\n", "\n", "\n", - "idx = np.argmin(np.abs(snr-np.median(snr)))\n", + "idx = np.argmin(np.abs(snr - np.median(snr)))\n", "# choose a voxel of medium level SNR.\n", - "fig = plt.figure(num=None, figsize=(12, 4), dpi=150, facecolor='w', edgecolor='k')\n", + "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", "noise_plot, = plt.plot(noise[:,idx],'g')\n", "signal_plot, = plt.plot(signal[:,idx],'r')\n", "plt.legend([noise_plot, signal_plot], ['noise', 'signal'])\n", - "plt.title('simulated data in an example voxel with pseudo-SNR of {}'.format(snr[idx]))\n", + "plt.title('simulated data in an example voxel'\n", + " ' with pseudo-SNR of {}'.format(snr[idx]))\n", "plt.xlabel('time')\n", "plt.show()\n", "\n", - "fig = plt.figure(num=None, figsize=(12, 4), dpi=150, facecolor='w', edgecolor='k')\n", + "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", "data_plot, = plt.plot(Y[:,idx],'b')\n", "plt.legend([data_plot], ['observed data'])\n", "plt.xlabel('time')\n", @@ -332,7 +371,7 @@ "plt.colorbar()\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", - "plt.title('pseudo-SNR')\n", + "plt.title('pseudo-SNR in a square \"ROI\"')\n", "plt.show()" ] }, @@ -340,14 +379,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### The reason that the pseudo-SNR in the example voxel is not too small, while the signal looks much smaller is because we happen to have low amplitudes in our design matrix. The True SNR depends on both the amplitudes in design matrix and the pseudo-SNR. Therefore, be aware that pseudo-SNR does not directly reflects how much signal the data have, but rather a map indicating the relative strength of signal in differerent voxels." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### When you have multiple runs, the noise won't be correlated between runs. Therefore, you should tell BRSA when is the onset of each scan" + "#### The reason that the pseudo-SNR in the example voxel is not too small, while the signal looks much smaller is because we happen to have low amplitudes in our design matrix. The true SNR depends on both the amplitudes in design matrix and the pseudo-SNR. Therefore, be aware that pseudo-SNR does not directly reflects how much signal the data have, but rather a map indicating the relative strength of signal in differerent voxels.\n", + "#### When you have multiple runs, the noise won't be correlated between runs. Therefore, you should tell BRSA when is the onset of each scan. \n", + "#### Note that the data (variable Y above) you feed to BRSA is the concatenation of data from all runs along the time dimension, as a 2-D matrix of time x space" ] }, { @@ -358,7 +392,7 @@ }, "outputs": [], "source": [ - "scan_onsets = np.linspace(0,design.n_TR,num=n_run+1)[:-1]\n", + "scan_onsets = np.linspace(0, design.n_TR,num=n_run + 1)[: -1]\n", "print('scan onsets: {}'.format(scan_onsets))" ] }, @@ -366,7 +400,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# (2) Fit Bayesian RSA to our simulated data" + "# Fit Bayesian RSA to our simulated data" ] }, { @@ -377,20 +411,24 @@ }, "outputs": [], "source": [ - "brsa = BRSA(GP_space=True,GP_inten=True,tau_range=10)\n", - "# Initiate an instance, telling it that we want to impose Gaussian Process prior over both space and intensity.\n", - "\n", - "brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets,\n", - " coords=coords_flat, inten=inten)\n", - "# The data to fit should be given to the argument X. Design matrix goes to design. And so on.\n" + "brsa = BRSA(GP_space=True, GP_inten=True,\n", + " tau_range=10, n_nureg=10)\n", + "# Initiate an instance, telling it\n", + "# that we want to impose Gaussian Process prior\n", + "# over both space and intensity.\n", + "\n", + "brsa.fit(X=Y, design=design.design_task,\n", + " coords=coords_flat, inten=inten, scan_onsets=scan_onsets)\n", + "# The data to fit should be given to the argument X.\n", + "# Design matrix goes to design. And so on.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### We can have a look at the estimated similarity in matrix brsa.C_ \n", - "### We can also compare the ideal covariance above with the one recovered, brsa.U_" + "### We can have a look at the estimated similarity in matrix brsa.C_. \n", + "#### We can also compare the ideal covariance above with the one recovered, brsa.U_" ] }, { @@ -409,7 +447,7 @@ "ax = plt.gca()\n", "ax.set_aspect(1)\n", "plt.title('Estimated correlation structure\\n shared between voxels\\n'\n", - " 'This constitutes the output of BRSA\\n')\n", + " 'This constitutes the output of Bayesian RSA\\n')\n", "plt.show()\n", "\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", @@ -427,8 +465,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## In contrast, we can have a look of the similarity matrix based on Pearson correlation between point estimates of betas of different conditions.\n", - "## This is what vanila RSA might give" + "### In contrast, we can have a look of the similarity matrix based on Pearson correlation between point estimates of betas of different conditions.\n", + "#### This is what vanila RSA might give" ] }, { @@ -439,10 +477,11 @@ }, "outputs": [], "source": [ - "regressor = np.insert(design.design_used,0,1,axis=1)\n", + "regressor = np.insert(design.design_task,\n", + " 0, 1, axis=1)\n", "betas_point = np.linalg.lstsq(regressor, Y)[0]\n", - "point_corr = np.corrcoef(betas_point[1:,:])\n", - "point_cov = np.cov(betas_point[1:,:])\n", + "point_corr = np.corrcoef(betas_point[1:, :])\n", + "point_cov = np.cov(betas_point[1:, :])\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(point_corr, vmin=-0.1, vmax=1)\n", "plt.xlim([0, 16])\n", @@ -490,7 +529,8 @@ "plt.show()\n", "\n", "fig = plt.figure(num=None, figsize=(5, 5), dpi=100)\n", - "plt.pcolor(np.reshape(snr / np.exp(np.mean(np.log(snr))), [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", + "plt.pcolor(np.reshape(snr / np.exp(np.mean(np.log(snr))),\n", + " [ROI_edge, ROI_edge]), vmin=0, vmax=5)\n", "plt.colorbar()\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", @@ -510,9 +550,12 @@ "RMS_RSA = np.mean((point_corr - ideal_corr)**2)**0.5\n", "print('RMS error of Bayesian RSA: {}'.format(RMS_BRSA))\n", "print('RMS error of standard RSA: {}'.format(RMS_RSA))\n", - "print('Recovered spatial smoothness length scale: {}, vs. true value: {}'.format(brsa.lGPspace_, smooth_width))\n", - "print('Recovered intensity smoothness length scale: {}, vs. true value: {}'.format(brsa.lGPinten_, inten_kernel))\n", - "print('Recovered standard deviation of GP prior: {}, vs. true value: {}'.format(brsa.bGP_, tau))" + "print('Recovered spatial smoothness length scale: '\n", + " '{}, vs. true value: {}'.format(brsa.lGPspace_, smooth_width))\n", + "print('Recovered intensity smoothness length scale: '\n", + " '{}, vs. true value: {}'.format(brsa.lGPinten_, inten_kernel))\n", + "print('Recovered standard deviation of GP prior: '\n", + " '{}, vs. true value: {}'.format(brsa.bGP_, tau))" ] }, { @@ -522,6 +565,13 @@ "#### Empirically, the smoothness turns to be over-estimated when signal is weak." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### We can also look at how other parameters are recovered." + ] + }, { "cell_type": "code", "execution_count": null, @@ -530,14 +580,68 @@ }, "outputs": [], "source": [ - "plt.scatter(brsa.sigma_, noise_level)\n", + "plt.scatter(noise_level * np.sqrt(0.1), brsa.sigma_)\n", + "plt.xlabel('true \"independent\" noise level')\n", + "plt.ylabel('recovered \"independent\" noise level')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", "plt.show()\n", - "plt.scatter(brsa.rho_, rho1)\n", + "\n", + "plt.scatter(rho1, brsa.rho_)\n", + "plt.xlabel('true AR(1) coefficients')\n", + "plt.ylabel('recovered AR(1) coefficients')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", "plt.show()\n", - "plt.scatter(brsa.nSNR_, snr)\n", + "\n", + "plt.scatter(np.log(snr) - np.mean(np.log(snr)),\n", + " np.log(brsa.nSNR_))\n", + "plt.xlabel('true normalized log SNR')\n", + "plt.ylabel('recovered log pseudo-SNR')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Even though the variation reduced in estimated pseudo-SNR (due to overestimation of smoothness of the GP prior under low SNR situation), betas recovered by the model has higher correlation with true betas than doing simple regression, shown below. Obiously there is shrinkage of the estimated betas, as a result of variance-bias tradeoff. But we think such shrinkage does preserve the patterns of betas, and therefore the result is suitable to be further used for decoding purpose." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.scatter(betas_simulated, brsa.beta_)\n", + "plt.xlabel('true betas (response amplitudes)')\n", + "plt.ylabel('recovered betas by Bayesian RSA')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", + "plt.show()\n", + "\n", + "\n", + "plt.scatter(betas_simulated, betas_point[1:, :])\n", + "plt.xlabel('true betas (response amplitudes)')\n", + "plt.ylabel('recovered betas by simple regression')\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", "plt.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The singular decomposition of noise, and the comparison between the first principal component of noise and the first principal component returned by the model." + ] + }, { "cell_type": "code", "execution_count": null, @@ -545,7 +649,23 @@ "collapsed": false }, "outputs": [], - "source": [] + "source": [ + "u, s, v = np.linalg.svd(noise)\n", + "plt.plot(s)\n", + "plt.xlabel('principal component')\n", + "plt.ylabel('singular value of simulated noise')\n", + "plt.show()\n", + "\n", + "plt.pcolor(np.reshape(v[0,:], [ROI_edge, ROI_edge]))\n", + "plt.title('Weights of the first principal component in noise')\n", + "plt.show()\n", + "\n", + "\n", + "plt.pcolor(np.reshape(brsa.beta0_[0,:], [ROI_edge, ROI_edge]))\n", + "plt.title('Weights of the first recovered principal component in noise')\n", + "plt.show()\n", + "print(brsa.beta0_.shape)" + ] } ], "metadata": { diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index 903a9b3a3..9be16e5e8 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -27,7 +27,7 @@ def test_can_instantiate(): features = 3 s = brainiak.reprsimil.brsa.BRSA(n_iter=50, rank=5, GP_space=True, GP_inten=True, tol=2e-3,\ - epsilon=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) + eta=0.001,space_smooth_range=10.0,inten_smooth_range=100.0) assert s, "Invalid BRSA instance!" def test_fit(): @@ -43,12 +43,12 @@ def test_fit(): # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,1:17],[4,1]) + design.design_task = np.tile(design.design_task[:,:-1],[4,1]) design.n_TR = design.n_TR * 4 # start simulating some data - n_V = 300 - n_C = np.size(design.design_used,axis=1) + n_V = 200 + n_C = np.size(design.design_task,axis=1) n_T = design.n_TR noise_bot = 0.5 @@ -67,10 +67,16 @@ def test_fit(): for i_t in range(1,n_T): noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level + noise = noise + np.random.rand(n_V) + # Random baseline + # ideal covariance matrix ideal_cov = np.zeros([n_C,n_C]) ideal_cov = np.eye(n_C)*0.6 - ideal_cov[5:9,5:9] = 0.6 + ideal_cov[0:4,0:4] = 0.2 + for cond in range(0,4): + ideal_cov[cond,cond] = 2 + ideal_cov[5:9,5:9] = 0.9 for cond in range(5,9): ideal_cov[cond,cond] = 1 idx = np.where(np.sum(np.abs(ideal_cov),axis=0)>0)[0] @@ -101,7 +107,7 @@ def test_fit(): snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level sqrt_v = noise_level*snr betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v - signal = np.dot(design.design_used,betas_simulated) + signal = np.dot(design.design_task,betas_simulated) # Adding noise to signal as data Y = signal + noise @@ -111,22 +117,23 @@ def test_fit(): # Test fitting with GP prior. - brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200) + brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,auto_nuiance=False) # We also test that it can detect baseline regressor included in the design matrix for task conditions - wrong_design = np.insert(design.design_used, 0, 1, axis=1) + wrong_design = np.insert(design.design_task, 0, 1, axis=1) with pytest.raises(ValueError) as excinfo: brsa.fit(X=Y, design=wrong_design, scan_onsets=scan_onsets, coords=coords, inten=inten) assert 'Your design matrix appears to have included baseline time series.' in str(excinfo.value) # Now we fit with the correct design matrix. - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, + brsa.fit(X=Y, design=design.design_task, scan_onsets=scan_onsets, coords=coords, inten=inten) # Check that result is significantly correlated with the ideal covariance matrix - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + u_b = brsa.U_ + u_i = ideal_cov + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b)], + u_i[np.tril_indices_from(u_i)])[1] assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] @@ -137,14 +144,15 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" - # Test fitting with lower rank + + # Test fitting with lower rank and without GP prior rank = n_C - 1 - brsa = BRSA(rank=rank) - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, - coords=coords, inten=inten) - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + n_nureg = 1 + brsa = BRSA(rank=rank,n_nureg=n_nureg) + brsa.fit(X=Y, design=design.design_task, scan_onsets=scan_onsets) + u_b = brsa.U_ + u_i = ideal_cov + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b)],u_i[np.tril_indices_from(u_i)])[1] assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] @@ -155,34 +163,20 @@ def test_fit(): p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" - # Test fitting without GP prior. - brsa = BRSA() - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets) - - # Check that result is significantly correlated with the ideal covariance matrix - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] - assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" - # check that the recovered SNRs makes sense - p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" - assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" - p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" - p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" assert not hasattr(brsa,'bGP_') and not hasattr(brsa,'lGPspace_') and not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of GP if GP is not requested.' # GP parameters are not set if not requested + assert brsa.beta0_.shape[0] == n_nureg, 'Shape of beta0 incorrect' + p = scipy.stats.pearsonr(brsa.beta0_[0,:],np.mean(noise,axis=0))[1] + assert p < 0.05, 'recovered beta0 does not correlate with the baseline of voxels.' # Test fitting with GP over just spatial coordinates. brsa = BRSA(GP_space=True) - brsa.fit(X=Y, design=design.design_used, scan_onsets=scan_onsets, coords=coords) + brsa.fit(X=Y, design=design.design_task, scan_onsets=scan_onsets, coords=coords) # Check that result is significantly correlated with the ideal covariance matrix - u_b = brsa.U_[1:,1:] - u_i = ideal_cov[1:,1:] - p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b,k=-1)],u_i[np.tril_indices_from(u_i,k=-1)])[1] + u_b = brsa.U_ + u_i = ideal_cov + p = scipy.stats.spearmanr(u_b[np.tril_indices_from(u_b)],u_i[np.tril_indices_from(u_i)])[1] assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] @@ -211,12 +205,12 @@ def test_gradient(): design = utils.ReadDesign(fname=file_path) n_run = 4 # concatenate it by 4 times, mimicking 4 runs of itenditcal timing - design.design_used = np.tile(design.design_used[:,1:17],[n_run,1]) + design.design_task = np.tile(design.design_task[:,:-1],[n_run,1]) design.n_TR = design.n_TR * n_run # start simulating some data n_V = 200 - n_C = np.size(design.design_used,axis=1) + n_C = np.size(design.design_task,axis=1) n_T = design.n_TR noise_bot = 0.5 @@ -270,7 +264,7 @@ def test_gradient(): snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level sqrt_v = noise_level*snr betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v - signal = np.dot(design.design_used,betas_simulated) + signal = np.dot(design.design_task,betas_simulated) # Adding noise to signal as data Y = signal + noise @@ -286,7 +280,7 @@ def test_gradient(): XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ X0TY, X0TDY, X0TFY, X0, n_run_returned, n_base =\ - brsa._prepare_data(design.design_used,Y,n_T,scan_onsets) + brsa._prepare_data(design.design_task,Y,n_T,scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ 'Dimension of XTY etc. returned from _prepare_data is wrong' @@ -344,17 +338,6 @@ def test_gradient(): param0_sing, vec) assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' - # We test the gradient to log(sigma^2) - # vec = np.zeros(np.size(param0_sing)) - # vec[idx_param_sing['log_sigma2']] = 1 - # dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_singpara(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - # XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, - # XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - # l_idx, n_C, n_T, n_V, n_run, n_base, - # idx_param_sing)[0], - # param0_sing, vec) - # assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt log(sigma2) is incorrect' - # We test the gradient to a1 vec = np.zeros(np.size(param0_sing)) vec[idx_param_sing['a1']] = 1 @@ -405,7 +388,7 @@ def test_gradient(): assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU incorrect' # We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior. - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ + X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL = \ brsa._calc_sandwidge(XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, @@ -414,15 +397,15 @@ def test_gradient(): XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, L_full, rho1, n_V, n_base) - assert np.ndim(XTAX) == 3, 'Dimension of XTAX is wrong by _calc_sandwidge()' - assert XTAY.shape == XTY.shape, 'Shape of XTAY is wrong by _calc_sandwidge()' - assert YTAY.shape == YTY_diag.shape, 'Shape of YTAY is wrong by _calc_sandwidge()' - assert np.ndim(X0TAX0) == 3, 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' - assert np.ndim(XTAX0) == 3, 'Dimension of XTAX0 is wrong by _calc_sandwidge()' + assert np.shape(XTAcorrX) == (n_V, n_C, n_C), 'Dimension of XTAcorrX is wrong by _calc_sandwidge()' + assert XTAcorrY.shape == XTY.shape, 'Shape of XTAcorrY is wrong by _calc_sandwidge()' + assert YTAcorrY.shape == YTY_diag.shape, 'Shape of YTAcorrY is wrong by _calc_sandwidge()' + assert np.shape(X0TAX0) == (n_V, n_base, n_base), 'Dimension of X0TAX0 is wrong by _calc_sandwidge()' + assert np.shape(XTAX0) == (n_V, n_C, n_base), 'Dimension of XTAX0 is wrong by _calc_sandwidge()' assert X0TAY.shape == X0TY.shape, 'Shape of X0TAX0 is wrong by _calc_sandwidge()' assert np.all(np.isfinite(X0TAX0_i)), 'Inverse of X0TAX0 includes NaN or Inf' ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV[idx_param_fitV['log_SNR2']], - XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -430,7 +413,7 @@ def test_gradient(): idx_param_fitV,n_C,False,False) vec = np.zeros(np.size(param0_fitV[idx_param_fitV['log_SNR2']])) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -440,7 +423,7 @@ def test_gradient(): assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' # We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior. - ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -449,7 +432,7 @@ def test_gradient(): dist2,inten_diff2,100,100) vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['log_SNR2'][0]] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -462,7 +445,7 @@ def test_gradient(): # We test the graident wrt spatial length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_space']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -475,7 +458,7 @@ def test_gradient(): # We test the graident wrt intensity length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) vec[idx_param_fitV['c_inten']] = 1 - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), @@ -488,7 +471,7 @@ def test_gradient(): # We test the graident on a random direction vec = np.random.randn(np.size(param0_fitV)) vec = vec / np.linalg.norm(vec) - dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, XTAX, XTAY, YTAY, X0TAX0, XTAX0, X0TAY, + dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitV(x, X0TAX0, XTAX0, X0TAY, X0TAX0_i, XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL, L_full[l_idx], np.tan(rho1*np.pi/2), diff --git a/tests/utils/test_utils.py b/tests/utils/test_utils.py index 74def6821..952a03942 100644 --- a/tests/utils/test_utils.py +++ b/tests/utils/test_utils.py @@ -83,8 +83,18 @@ def test_ReadDesign(): import numpy as np import os.path file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") - design = ReadDesign(fname=file_path) + design = ReadDesign(fname=file_path, include_orth=False, include_pols=False) assert design, 'Failed to read design matrix' + assert design.reg_nuiance is None, \ + 'Nuiance regressor is not None when include_orth and include_pols are'\ + ' both set to False' read = ReadDesign() assert read, 'Failed to initialize an instance of the class' - + design = ReadDesign(fname=file_path, include_orth=True, include_pols=True) + assert np.size(design.cols_nuisance) == 10, \ + 'Mistake in counting the number of nuiance regressors' + assert np.size(design.cols_task) == 17, \ + 'Mistake in counting the number of task conditions' + assert np.shape(design.reg_nuiance)[0] == np.shape(design.design_task)[0],\ + 'The number of time points in nuiance regressor does not match'\ + ' that of task response' From 070022e9c7ddd24ea55a533c40160a512543b347 Mon Sep 17 00:00:00 2001 From: lcnature Date: Wed, 12 Oct 2016 00:43:46 -0400 Subject: [PATCH 15/30] fixed some bugs and typos --- tests/reprsimil/test_brsa.py | 29 +++++++++++------------------ tests/utils/test_utils.py | 4 ++-- 2 files changed, 13 insertions(+), 20 deletions(-) diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index 9be16e5e8..203c51cec 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -137,12 +137,12 @@ def test_fit(): assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert p < 0.01, "Fitted SNR does not correlate with simulated SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + assert p < 0.01, "Fitted noise level does not correlate with simulated noise level!" p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simulated values!" # Test fitting with lower rank and without GP prior @@ -156,12 +156,12 @@ def test_fit(): assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert p < 0.01, "Fitted SNR does not correlate with simulated SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + assert p < 0.01, "Fitted noise level does not correlate with simulated noise level!" p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simulated values!" assert not hasattr(brsa,'bGP_') and not hasattr(brsa,'lGPspace_') and not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of GP if GP is not requested.' @@ -180,12 +180,12 @@ def test_fit(): assert p < 0.01, "Fitted covariance matrix does not correlate with ideal covariance matrix!" # check that the recovered SNRs makes sense p = scipy.stats.pearsonr(brsa.nSNR_,snr)[1] - assert p < 0.01, "Fitted SNR does not correlate with simualted SNR!" + assert p < 0.01, "Fitted SNR does not correlate with simulated SNR!" assert np.isclose(np.mean(np.log(brsa.nSNR_)),0), "nSNR_ not normalized!" p = scipy.stats.pearsonr(brsa.sigma_,noise_level)[1] - assert p < 0.01, "Fitted noise level does not correlate with simualted noise level!" + assert p < 0.01, "Fitted noise level does not correlate with simulated noise level!" p = scipy.stats.pearsonr(brsa.rho_,rho1)[1] - assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simualted values!" + assert p < 0.01, "Fitted AR(1) coefficient does not correlate with simulated values!" assert not hasattr(brsa,'lGPinten_'),\ 'the BRSA object should not have parameters of lGPinten_ if only smoothness in space is requested.' # GP parameters are not set if not requested @@ -241,9 +241,6 @@ def test_gradient(): # generating signal snr_level = 5.0 # test with high SNR - # snr = np.random.rand(n_V)*(snr_top-snr_bot)+snr_bot - # Notice that accurately speaking this is not snr. the magnitude of signal depends - # not only on beta but also on x. inten = np.random.randn(n_V) * 20.0 # parameters of Gaussian process to generate pseuso SNR @@ -262,6 +259,8 @@ def test_gradient(): L = np.linalg.cholesky(K) snr = np.exp(np.dot(L,np.random.randn(n_V))) * snr_level + # Notice that accurately speaking this is not snr. the magnitude of signal depends + # not only on beta but also on x. sqrt_v = noise_level*snr betas_simulated = np.dot(L_full,np.random.randn(n_C,n_V)) * sqrt_v signal = np.dot(design.design_task,betas_simulated) @@ -269,10 +268,8 @@ def test_gradient(): # Adding noise to signal as data Y = signal + noise - scan_onsets = np.linspace(0,design.n_TR,num=n_run+1) - # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,rank=n_C) @@ -296,9 +293,6 @@ def test_gradient(): 'Dimension of X0TY etc. returned from _prepare_data is wrong' X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) - # rank = n_C - 1 - # idx_rank = np.where(l_idx[1] < rank) - # l_idx = (l_idx[0][idx_rank], l_idx[1][idx_rank]) n_l = np.size(l_idx[0]) # Make sure all the fields are in the indices. @@ -315,7 +309,6 @@ def test_gradient(): param0_fitU = np.random.randn(n_l+n_V) * 0.1 param0_fitV = np.random.randn(n_V+1) * 0.1 param0_sing = np.random.randn(n_l+1) * 0.1 - # param0_sing[idx_param_sing['log_sigma2']] += np.mean(np.log(noise_level)) * 2 param0_sing[idx_param_sing['a1']] += np.mean(np.tan(rho1 * np.pi / 2)) param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 diff --git a/tests/utils/test_utils.py b/tests/utils/test_utils.py index 952a03942..760b86fbe 100644 --- a/tests/utils/test_utils.py +++ b/tests/utils/test_utils.py @@ -85,7 +85,7 @@ def test_ReadDesign(): file_path = os.path.join(os.path.dirname(__file__), "example_design.1D") design = ReadDesign(fname=file_path, include_orth=False, include_pols=False) assert design, 'Failed to read design matrix' - assert design.reg_nuiance is None, \ + assert design.reg_nuisance is None, \ 'Nuiance regressor is not None when include_orth and include_pols are'\ ' both set to False' read = ReadDesign() @@ -95,6 +95,6 @@ def test_ReadDesign(): 'Mistake in counting the number of nuiance regressors' assert np.size(design.cols_task) == 17, \ 'Mistake in counting the number of task conditions' - assert np.shape(design.reg_nuiance)[0] == np.shape(design.design_task)[0],\ + assert np.shape(design.reg_nuisance)[0] == np.shape(design.design_task)[0],\ 'The number of time points in nuiance regressor does not match'\ ' that of task response' From 3ccefe37a7a0bbfb51ce855282edcbdbe7eb365d Mon Sep 17 00:00:00 2001 From: lcnature Date: Wed, 12 Oct 2016 16:02:00 -0400 Subject: [PATCH 16/30] Removed some redundant calculation" --- brainiak/reprsimil/brsa.py | 180 ++++++++++-------- ...tational_similarity_estimate_example.ipynb | 31 +-- tests/reprsimil/test_brsa.py | 25 ++- 3 files changed, 139 insertions(+), 97 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 23e41f8c0..448a1027f 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -78,24 +78,24 @@ class BRSA(BaseEstimator): (e.g., calculating the similarity matrix of responses to each event), you might want to start with specifying a lower rank and use metrics such as AIC or BIC to decide the optimal rank. - auto_nuiance: boolean, default: True + auto_nuisance: boolean, default: True In order to model spatial correlation between voxels that cannot be accounted for by common response captured in the design matrix, we assume that a set of time courses not related to the task conditions are shared across voxels with unknown amplitudes. One approach is for users to provide time series which they consider - as nuiance but exist in the noise (such as head motion). + as nuisance but exist in the noise (such as head motion). The other way is to take the first n_nureg principal components in the residual after one fitting of the Bayesian RSA model, and use these components as the nuisance regressor. - If this flag is turned on, the nuiance regressor provided by the + If this flag is turned on, the nuisance regressor provided by the user is used only in the first round of fitting. The PCs from residuals will be used in the next round of fitting. - Note that nuiance regressor is not required from user. If it is - not provided, DC components for each run will be used as nuiance + Note that nuisance regressor is not required from user. If it is + not provided, DC components for each run will be used as nuisance regressor in the initial fitting. n_nureg: int, default: 6 - Number of nuiance regressors to use in order to model signals + Number of nuisance regressors to use in order to model signals shared across voxels not captured by the design matrix. This parameter will not be effective in the first round of fitting. GP_space: boolean, default: False @@ -178,7 +178,7 @@ class BRSA(BaseEstimator): def __init__( self, n_iter=50, rank=None, GP_space=False, GP_inten=False, - tol=2e-3, auto_nuiance=True, n_nureg=6, verbose=False, + tol=2e-3, auto_nuisance=True, n_nureg=6, verbose=False, eta=0.0001, space_smooth_range=None, inten_smooth_range=None, tau_range=10.0, init_iter=20, optimizer='BFGS', rand_seed=0): self.n_iter = n_iter @@ -186,7 +186,7 @@ def __init__( self.GP_space = GP_space self.GP_inten = GP_inten self.tol = tol - self.auto_nuiance = auto_nuiance + self.auto_nuisance = auto_nuisance self.n_nureg = n_nureg self.verbose = verbose self.eta = eta @@ -207,7 +207,7 @@ def __init__( self.rand_seed = rand_seed return - def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, + def fit(self, X, design, nuisance=None, scan_onsets=None, coords=None, inten=None): """Compute the Bayesian RSA @@ -223,12 +223,12 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, response for task conditions. You do not need to include regressors for a DC component or motion parameters, unless with a strong reason. If you want to model DC component or head motion, - you should include them in nuiance regressors. + you should include them in nuisance regressors. If you have multiple run, the design matrix of all runs should be concatenated along the time dimension, with one column across runs for each condition. - nuiance: optional, 2-D numpy array, - shape=[time_points, nuiance_factors] + nuisance: optional, 2-D numpy array, + shape=[time_points, nuisance_factors] The responses to these regressors will be marginalized out from each voxel, which means they are considered, but won't be assumed to share the same pseudo-SNR map with with the design matrix. @@ -236,14 +236,14 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, relative contribution of design matrix to each voxel. You can provide time courses such as those for head motion to this parameter. - Note that if auto_nuiance is set to True, this input + Note that if auto_nuisance is set to True, this input will only be used in the first round of fitting. The first n_nureg principal components of residual (excluding the response - to the design matrix) will be used as the nuiance regressor + to the design matrix) will be used as the nuisance regressor for the second round of fitting. - If auto_nuiance is set to False, the nuiance regressors supplied + If auto_nuisance is set to False, the nuisance regressors supplied by the users together with DC components will be used as - nuiance time series. + nuisance time series. scan_onsets: optional, an 1-D numpy array, shape=[runs,] This specifies the indices of X which correspond to the onset of each scanning run. For example, if you have two experimental @@ -296,16 +296,18 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, assert self.rank is None or self.rank <= design.shape[1],\ 'Your design matrix has fewer columns than the rank you set' - # Check the nuiance regressors. - if nuiance is not None: - assert_all_finite(nuiance) - assert np.linalg.matrix_rank(nuiance) == nuiance.shape[1], \ - 'The nuiance regressor has rank smaller than the number of'\ + # Check the nuisance regressors. + if nuisance is not None: + assert_all_finite(nuisance) + assert nuisance.ndim == 2,\ + 'The nuisance regressor should be 2 dimension ndarray' + assert np.linalg.matrix_rank(nuisance) == nuisance.shape[1], \ + 'The nuisance regressor has rank smaller than the number of'\ 'columns. Some columns can be explained by linear '\ - 'combination of other columns. Please check your nuiance' \ + 'combination of other columns. Please check your nuisance' \ 'regressors.' - assert np.size(nuiance, axis=0) == np.size(X, axis=0), \ - 'Nuiance regressor and data do not have the same '\ + assert np.size(nuisance, axis=0) == np.size(X, axis=0), \ + 'Nuisance regressor and data do not have the same '\ ' number of time points.' # check scan_onsets validity assert scan_onsets is None or\ @@ -348,7 +350,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, # without imposing any Gaussian Process prior on log(SNR^2) self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ self.sigma_, self.rho_ = \ - self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + self._fit_RSA_UV(X=design, Y=X, X0=nuisance, scan_onsets=scan_onsets) elif not self.GP_inten: # If GP_space is requested, but GP_inten is not, a GP prior @@ -356,7 +358,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ self.sigma_, self.rho_, self.lGPspace_, self.bGP_ \ = self._fit_RSA_UV( - X=design, Y=X, X0=nuiance, + X=design, Y=X, X0=nuisance, scan_onsets=scan_onsets, coords=coords) else: # If both self.GP_space and self.GP_inten are True, @@ -364,7 +366,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, self.U_, self.L_, self.nSNR_, self.beta_, self.beta0_,\ self.sigma_, self.rho_, self.lGPspace_, self.bGP_,\ self.lGPinten_ = \ - self._fit_RSA_UV(X=design, Y=X, X0=nuiance, + self._fit_RSA_UV(X=design, Y=X, X0=nuisance, scan_onsets=scan_onsets, coords=coords, inten=inten) @@ -387,7 +389,7 @@ def fit(self, X, design, nuiance=None, scan_onsets=None, coords=None, # For example, in X'AX = X'(I + rho1*D + rho1**2*F)X / sigma2, # the products X'X, X'DX, X'FX, etc. can always be re-used if they # are pre-calculated. Therefore, _D_gen and _F_gen constructs matrices - # D and F, and _prepare_data calculates these products that can be + # D and F, and _prepare_data_* calculates these products that can be # re-used. In principle, once parameters have been fitted for a # dataset, they can be updated for new incoming data by adding the # products X'X, X'DX, X'FX, X'Y etc. from new data to those from @@ -409,16 +411,12 @@ def _F_gen(self, TR): else: return np.empty([0, 0]) - def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): - """Prepares different forms of products of design matrix X and data Y, - or between themselves. These products are reused a lot during fitting. - So we pre-calculate them. Because of the fact that these are reused, - it is in principle possible to update the fitting as new data come in, - by just incrementally adding the products of new data and - their corresponding part of design matrix - no_DC means not inserting regressors for DC components into nuiance - regressor. It will only take effect if X0 is not None. - """ + def _prepare_DF(self, n_T, scan_onsets=None): + """ Prepare the essential template matrices D and F for + pre-calculating some terms to be re-used. + The inverse covariance matrix of AR(1) noise is + sigma^-2 * (I - rho1*D + rho1**2 * F). + And we denote A = I - rho1*D + rho1**2 * F""" if scan_onsets is None: # assume that all data are acquired within the same scan. D = np.diag(np.ones(n_T - 1), -1) + np.diag(np.ones(n_T - 1), 1) @@ -450,7 +448,18 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): F = scipy.linalg.block_diag(F, f_ele) # D and F above are templates for constructing # the inverse of temporal covariance matrix of noise - + return D, F, run_TRs, n_run + + def _prepare_data_XY(self, X, Y, D, F): + """Prepares different forms of products of design matrix X + and data Y, or between themselves. + These products are re-used a lot during fitting. + So we pre-calculate them. Because these are reused, + it is in principle possible to update the fitting + as new data come in, by just incrementally adding + the products of new data and their corresponding parts + of design matrix to these pre-calculated terms. + """ XTY, XTDY, XTFY = self._make_templates(D, F, X, Y) YTY_diag = np.sum(Y * Y, axis=0) @@ -459,6 +468,19 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): XTX, XTDX, XTFX = self._make_templates(D, F, X, X) + return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX + + def _prepare_data_XYX0(self, X, Y, X0, D, F, run_TRs, no_DC=False): + """Prepares different forms of products between design matrix X or + data Y or nuisance regressors X0 and X0. + These products are re-used a lot during fitting. + So we pre-calculate them. + no_DC means not inserting regressors for DC components + into nuisance regressor. + It will only take effect if X0 is not None. + """ + X_base = [] for r_l in run_TRs: X_base = scipy.linalg.block_diag(X_base, np.ones(r_l)[:, None]) @@ -494,9 +516,8 @@ def _prepare_data(self, X, Y, n_T, scan_onsets=None, X0=None, no_DC=True): XTX0, XTDX0, XTFX0 = self._make_templates(D, F, X, X0) X0TY, X0TDY, X0TFY = self._make_templates(D, F, X0, Y) - return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base + return X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base def _make_sandwidge(self, XTX, XTDX, XTFX, rho1): return XTX - rho1 * XTDX + rho1**2 * XTFX @@ -700,15 +721,18 @@ def _fit_RSA_UV(self, X, Y, X0, n_l = np.size(l_idx[0]) # the number of parameters for L + D, F, run_TRs, n_run = self._prepare_DF( + n_T, scan_onsets=scan_onsets) XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - X0=X0, no_DC=False) + XTDX, XTFX = self._prepare_data_XY(X, Y, D, F) + + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=False) # Prepare the data for fitting. These pre-calculated matrices # will be re-used a lot in evaluating likelihood function and # gradient. - # DC component will be added to the nuiance regressors. + # DC component will be added to the nuisance regressors. # In later steps, we do not need to add DC components again dist2, inten_diff2, space_smooth_range, inten_smooth_range,\ @@ -760,11 +784,10 @@ def _fit_RSA_UV(self, X, Y, X0, # Step 2 fitting, which only happens if # GP prior is requested if GP_space: - current_vec_U_chlsk_l, current_a1, current_logSNR2 \ + current_vec_U_chlsk_l, current_a1, current_logSNR2, X0 \ = self._fit_diagV_noGP( XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, @@ -794,14 +817,15 @@ def _fit_RSA_UV(self, X, Y, X0, # which might render 5 percential to 0. # Step 3 fitting. GP prior is imposed if requested. - # In this step, unless auto_nuiance is set to False, X0 + # In this step, unless auto_nuisance is set to False, X0 # will be re-estimated from the residuals after each step # of fitting. logger.debug('indexing:{}'.format(idx_param_fitV)) logger.debug('initial GP parameters:{}'.format(current_GP)) current_vec_U_chlsk_l, current_a1, current_logSNR2,\ current_GP, X0 = self._fit_diagV_GP( - X, Y, scan_onsets, X0, + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, @@ -819,11 +843,9 @@ def _fit_RSA_UV(self, X, Y, X0, # Calculating est_sigma_AR1_UV, est_sigma_AR1_UV, # est_beta_AR1_UV and est_beta0_AR1_UV - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - X0=X0, no_DC=True) + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=True) X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ XTAcorrX, XTAcorrY, YTAcorrY, LTXTAcorrY, XTAcorrXL, LTXTAcorrXL\ @@ -958,8 +980,7 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, def _fit_diagV_noGP( self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, - XTX, XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, idx_param_fitU, idx_param_fitV, @@ -987,12 +1008,10 @@ def _fit_diagV_noGP( L = np.zeros((n_C, rank)) tol = self.tol * 5 for it in range(0, init_iter): + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=True) # fit V, reflected in the log(SNR^2) of each voxel - # XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - # XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - # X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - # = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - # X0=X0) rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ @@ -1026,7 +1045,7 @@ def _fit_diagV_noGP( '{}'.format(norm_fitVchange)) logger.debug('E[log(SNR2)^2]:'.format(np.mean(current_logSNR2**2))) - # The below lines are for debugging purpose. + # The lines below are for debugging purpose. # If any voxel's log(SNR^2) gets to non-finite number, # something might be wrong -- could be that the data has # nothing to do with the design matrix. @@ -1060,14 +1079,28 @@ def _fit_diagV_noGP( '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() + # Re-estimating X0 from residuals + current_SNR2 = np.exp(current_logSNR2) + if self.auto_nuisance: + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, current_sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, current_SNR2, + n_V, n_T, n_run, rank, n_base) + betas = current_sigma2**0.5 * current_SNR2 \ + * np.dot(L, YTAcorrXL_LAMBDA.T) + residuals = Y - np.dot(X, betas) + u, s, v = np.linalg.svd(residuals) + X0 = u[:, :self.n_nureg] + if norm_fitVchange / np.sqrt(param0_fitV.size) < tol \ and norm_fitUchange / np.sqrt(param0_fitU.size) \ < tol: break - return current_vec_U_chlsk_l, current_a1, current_logSNR2 + return current_vec_U_chlsk_l, current_a1, current_logSNR2, X0 def _fit_diagV_GP( - self, X, Y, scan_onsets, X0, + self, XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, + XTX, XTDX, XTFX, X, Y, X0, D, F, run_TRs, current_vec_U_chlsk_l, current_a1, current_logSNR2, current_GP, n_smooth, idx_param_fitU, idx_param_fitV, l_idx, @@ -1099,11 +1132,9 @@ def _fit_diagV_GP( param0_fitV[idx_param_fitV['c_both']] = current_GP.copy() for it in range(0, n_iter): - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run, n_base \ - = self._prepare_data(X, Y, n_T, scan_onsets=scan_onsets, - X0=X0, no_DC=True) + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( + X, Y, X0, D, F, run_TRs, no_DC=True) # fit V rho1 = np.arctan(current_a1) * 2 / np.pi X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ @@ -1172,10 +1203,9 @@ def _fit_diagV_GP( '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() - current_SNR2 = np.exp(current_logSNR2) - # Re-estimating X0 from residuals - if self.auto_nuiance: + current_SNR2 = np.exp(current_logSNR2) + if self.auto_nuisance: LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, current_sigma2 \ = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, current_SNR2, diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index e78329a4f..d0d97cb9d 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -162,7 +162,9 @@ "K_noise = noise_level[:, np.newaxis] \\\n", " * (np.exp(-dist2 / noise_smooth_width**2 / 2.0) \\\n", " + np.eye(n_V) * 0.1) * noise_level\n", - "print(np.shape(K_noise))\n", + "# We make spatially correlated noise by generating\n", + "# noise at each time point from a Gaussian Process\n", + "# defined over the coordinates.\n", "plt.pcolor(K_noise)\n", "plt.colorbar()\n", "plt.xlim([0, ROI_edge * ROI_edge])\n", @@ -176,13 +178,9 @@ "for i_t in range(1, n_T):\n", " noise[i_t, :] = noise[i_t - 1, :] * rho1 \\\n", " + np.dot(L_noise,np.random.randn(n_V))\n", - "\n", - "\n", - "# noise = np.zeros([n_T,n_V])\n", - "# noise[0,:] = np.random.randn(n_V) * noise_level / np.sqrt(1-rho1**2)\n", - "# for i_t in range(1,n_T):\n", - "# noise[i_t,:] = noise[i_t-1,:] * rho1 + np.random.randn(n_V) * noise_level\n", - "# Here, we assume noise is independent between voxels\n", + "# For each voxel, the noise follows AR(1) process:\n", + "# fresh noise plus a dampened version of noise at\n", + "# the previous time point.\n", "noise = noise + np.random.randn(n_V)\n", "fig = plt.figure(num=None, figsize=(12, 2), dpi=150,\n", " facecolor='w', edgecolor='k')\n", @@ -313,10 +311,6 @@ "# then the smoothness has much small dependency on the intensity.\n", "\n", "\n", - "# coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", - "# coords_flat = np.reshape(coords,[3, n_V]).T\n", - "# dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", - "\n", "inten = np.random.rand(n_V) * 20.0\n", "# For simplicity, we just assume that the intensity\n", "# of all voxels are uniform distributed between 0 and 20\n", @@ -580,11 +574,13 @@ }, "outputs": [], "source": [ - "plt.scatter(noise_level * np.sqrt(0.1), brsa.sigma_)\n", + "plt.scatter(noise_level * np.sqrt(0.1/1.1), brsa.sigma_)\n", "plt.xlabel('true \"independent\" noise level')\n", "plt.ylabel('recovered \"independent\" noise level')\n", "ax = plt.gca()\n", "ax.set_aspect(1)\n", + "ax.set_xticks(np.arange(0.1,0.7,0.1))\n", + "ax.set_yticks(np.arange(0.1,0.7,0.1))\n", "plt.show()\n", "\n", "plt.scatter(rho1, brsa.rho_)\n", @@ -666,6 +662,15 @@ "plt.show()\n", "print(brsa.beta0_.shape)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index 203c51cec..cfb832434 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -117,7 +117,7 @@ def test_fit(): # Test fitting with GP prior. - brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,auto_nuiance=False) + brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,auto_nuisance=False) # We also test that it can detect baseline regressor included in the design matrix for task conditions wrong_design = np.insert(design.design_task, 0, 1, axis=1) @@ -273,13 +273,19 @@ def test_gradient(): # Test fitting with GP prior. brsa = BRSA(GP_space=True,GP_inten=True,verbose=False,n_iter = 200,rank=n_C) - # test if the gradients are correct - XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ - XTDX, XTFX, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ - X0TY, X0TDY, X0TFY, X0, n_run_returned, n_base =\ - brsa._prepare_data(design.design_task,Y,n_T,scan_onsets) + # Additionally, we test the generation of re-used terms. + X0 = np.ones(n_T)[:, None] + D, F, run_TRs, n_run_returned = brsa._prepare_DF( + n_T, scan_onsets=scan_onsets) assert n_run_returned == n_run, 'There is mistake in counting number of runs' - assert np.ndim(XTY) == 2 and np.ndim(XTDY) == 2 and np.ndim(XTFY) == 2,\ + assert np.sum(run_TRs) == n_T, 'The segmentation of the total experiment duration is wrong' + XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \ + XTDX, XTFX = brsa._prepare_data_XY(design.design_task, Y, D, F) + X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ + X0TY, X0TDY, X0TFY, X0, n_base = brsa._prepare_data_XYX0( + design.design_task, Y, X0, D, F, run_TRs, no_DC=False) + assert np.shape(XTY) == (n_C, n_V) and np.shape(XTDY) == (n_C, n_V) \ + and np.shape(XTFY) == (n_C, n_V),\ 'Dimension of XTY etc. returned from _prepare_data is wrong' assert np.ndim(YTY_diag) == 1 and np.ndim(YTDY_diag) == 1 and np.ndim(YTFY_diag) == 1,\ 'Dimension of YTY_diag etc. returned from _prepare_data is wrong' @@ -291,10 +297,10 @@ def test_gradient(): 'Dimension of XTX0 etc. returned from _prepare_data is wrong' assert np.ndim(X0TY) == 2 and np.ndim(X0TDY) == 2 and np.ndim(X0TFY) == 2,\ 'Dimension of X0TY etc. returned from _prepare_data is wrong' - X0 = np.ones(n_T) l_idx = np.tril_indices(n_C) n_l = np.size(l_idx[0]) + # Make sure all the fields are in the indices. idx_param_sing, idx_param_fitU, idx_param_fitV = brsa._build_index_param(n_l, n_V, 2) assert 'Cholesky' in idx_param_sing and 'a1' in idx_param_sing, \ @@ -313,7 +319,8 @@ def test_gradient(): param0_fitV[idx_param_fitV['log_SNR2']] += np.log(snr[:n_V-1])*2 param0_fitV[idx_param_fitV['c_space']] += np.log(smooth_width)*2 param0_fitV[idx_param_fitV['c_inten']] += np.log(inten_kernel)*2 - + + # test if the gradients are correct # log likelihood and derivative of the _singpara function ll0, deriv0 = brsa._loglike_AR1_singpara(param0_sing, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, From 899eb167ac2b5f9772bbfe08c9f0fb07fcd38969 Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 13 Oct 2016 11:01:45 -0400 Subject: [PATCH 17/30] Removing some unnecessary package in brsa example --- ...rsa_representational_similarity_estimate_example.ipynb | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index d0d97cb9d..0ac50725e 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -6,14 +6,16 @@ "collapsed": false }, "source": [ - "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset." + "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset.\n", + "Questions can be directed to mcai [ at ] princeton [ dot ] edu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "#### Load some package which we will use in this demo" + "#### Load some package which we will use in this demo.\n", + "If you see error related to loading any package, you can install that package. For example, if you use Anaconda, you can use \"conda install matplotlib\" to install matplotlib." ] }, { @@ -30,8 +32,6 @@ "import numpy as np\n", "from brainiak.reprsimil.brsa import BRSA\n", "import brainiak.utils.utils as utils\n", - "import os.path\n", - "import numdifftools as nd\n", "import matplotlib.pyplot as plt\n", "import logging\n", "np.random.seed(10)" From 40e337f74c7b0121d1227594aa30f3bcadda844f Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 13 Oct 2016 12:05:25 -0400 Subject: [PATCH 18/30] adding comment on nuisance regressor --- .../brsa_representational_similarity_estimate_example.ipynb | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 0ac50725e..c3ef74644 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -635,7 +635,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### The singular decomposition of noise, and the comparison between the first principal component of noise and the first principal component returned by the model." + "### The singular decomposition of noise, and the comparison between the first principal component of noise and the first principal component returned by the model.\n", + "Apparently one can imagine that the choice of the number of principal components used as nuisance regressors can influence the result. If you just choose 1 or 2, perhaps only the baseline and drift would be captured. But including too many nuisance regressors would slow the fitting speed and might have risk of overfitting. The users might consider starting in the range of 5-20. In future, we may consider using cross validation to determine the number of nuisance regressors, similar as in GLMdenoise (http://kendrickkay.net/GLMdenoise/)" ] }, { From 23f4fa9a5267d407e199147bb372d118016fd85c Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 13 Oct 2016 12:50:45 -0400 Subject: [PATCH 19/30] removing outdated note in brsa --- brainiak/reprsimil/brsa.py | 6 ------ 1 file changed, 6 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 448a1027f..9b758e012 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -168,12 +168,6 @@ class BRSA(BaseEstimator): lGPinten_: scalar, only if GP_inten is True the length scale in fMRI intensity of the GP prior of log(SNR) - Notes - ----- - The current version assumes noise is independent across voxels. - Real data typically has spatial correlation in noise. - This assumption might still introduce some bias in the result. - Spatial correlation will be included in a future version. """ def __init__( From 89408b66e0d00899f4290f182dad6cb991443289 Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 13 Oct 2016 12:57:29 -0400 Subject: [PATCH 20/30] updating docstring --- brainiak/reprsimil/brsa.py | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 9b758e012..02b55bd22 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -51,8 +51,8 @@ class BRSA(BaseEstimator): """Bayesian representational Similarity Analysis (BRSA) - Given the time series of preprocessed neural imaging data and - the hypothetical neural response (design matrix) to + Given the time series of neural imaging data in a region of interest + (ROI) and the hypothetical neural response (design matrix) to each experimental condition of interest, calculate the shared covariance matrix of the voxels(recording unit)' response to each condition, @@ -167,6 +167,12 @@ class BRSA(BaseEstimator): the length scale of Gaussian Process prior of log(SNR) lGPinten_: scalar, only if GP_inten is True the length scale in fMRI intensity of the GP prior of log(SNR) + beta_: array, shape=[conditions, voxels] + The maximum a posterior estimation of the response amplitudes + of each voxel to each task condition. + beta0_: array, shape=[n_nureg, voxels] + The loading weights of each voxel for the shared time courses + not captured by the design matrix. """ From 8c6a0cb0aeda17123291ba05f4b0b594dd3839ef Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 13 Oct 2016 13:10:11 -0400 Subject: [PATCH 21/30] a bit more changing of docstring --- brainiak/reprsimil/brsa.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 02b55bd22..0ba3441c7 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -86,8 +86,8 @@ class BRSA(BaseEstimator): One approach is for users to provide time series which they consider as nuisance but exist in the noise (such as head motion). The other way is to take the first n_nureg principal components - in the residual after one fitting of the Bayesian RSA model, and use - these components as the nuisance regressor. + in the residual after subtracting the response to the design matrix + from the data, and use these components as the nuisance regressor. If this flag is turned on, the nuisance regressor provided by the user is used only in the first round of fitting. The PCs from residuals will be used in the next round of fitting. From 86b4591389307840a9aa70080663c7b76c7d7357 Mon Sep 17 00:00:00 2001 From: lcnature Date: Thu, 13 Oct 2016 14:22:31 -0400 Subject: [PATCH 22/30] minor changes --- brainiak/reprsimil/brsa.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 0ba3441c7..70d7e0ebf 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -222,7 +222,7 @@ def fit(self, X, design, nuisance=None, scan_onsets=None, coords=None, This is the design matrix. It should only include the hypothetic response for task conditions. You do not need to include regressors for a DC component or motion parameters, unless with - a strong reason. If you want to model DC component or head motion, + a strong reason. If you want to model head motion, you should include them in nuisance regressors. If you have multiple run, the design matrix of all runs should be concatenated along the time dimension, @@ -231,7 +231,7 @@ def fit(self, X, design, nuisance=None, scan_onsets=None, coords=None, shape=[time_points, nuisance_factors] The responses to these regressors will be marginalized out from each voxel, which means they are considered, but won't be assumed - to share the same pseudo-SNR map with with the design matrix. + to share the same pseudo-SNR map with the design matrix. Therefore, the pseudo-SNR map will only reflect the relative contribution of design matrix to each voxel. You can provide time courses such as those for head motion @@ -308,7 +308,7 @@ def fit(self, X, design, nuisance=None, scan_onsets=None, coords=None, 'regressors.' assert np.size(nuisance, axis=0) == np.size(X, axis=0), \ 'Nuisance regressor and data do not have the same '\ - ' number of time points.' + 'number of time points.' # check scan_onsets validity assert scan_onsets is None or\ (np.max(scan_onsets) <= X.shape[0] and np.min(scan_onsets) >= 0),\ @@ -774,7 +774,7 @@ def _fit_RSA_UV(self, X, Y, X0, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - X, X0, Y, idx_param_sing, + X, Y, X0, idx_param_sing, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank) current_logSNR2 = -current_logSigma2 @@ -905,7 +905,7 @@ def _initial_fit_singpara(self, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - X, X0, Y, idx_param_sing, l_idx, + X, Y, X0, idx_param_sing, l_idx, n_C, n_T, n_V, n_l, n_run, n_base, rank): """ Perform initial fitting of a simplified model, which assumes that all voxels share exactly the same temporal covariance From b304ec1e6990bda6972d5579dc25fddec0755d32 Mon Sep 17 00:00:00 2001 From: lcnature Date: Fri, 14 Oct 2016 00:47:54 -0400 Subject: [PATCH 23/30] update the example for brsa --- ..._representational_similarity_estimate_example.ipynb | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index c3ef74644..8ea25bd4c 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -78,7 +78,8 @@ "\n", "We can use the utility called ReadDesign to read a design matrix generated from AFNI. For design matrix saved as Matlab data file by SPM or or other toolbox, you can use scipy.io.loadmat('YOURFILENAME') and extract the design matrix from the dictionary returned. Basically, the Bayesian RSA in this toolkit just needs a numpy array which is in size of {time points} * {condition}\n", "\n", - "The design matrix we load in this demo has 16 different conditions. The baseline level in different voxels might be different even if you z-score the data. Therefore, we need to take into account possible different baseline. Currently, our method put an additional condition composed of all 1's (DC component) into the design matrix for this goal. Very soon, we will have a version which treats baseline level and other not interested signals shared across voxels separately from the signals we are interested in.\n", + "In typical fMRI analysis, some nuisance regressors such as head motion, baseline time series and slow drift are also entered into regression. In using our method, you should not include such regressors into the design matrix, because the spatial spread of such nuisance regressors might be quite different from the spatial spread of task related signal. Including such nuisance regressors in design matrix might influence the pseudo-SNR map, which in turn influence the estimation of the shared covariance matrix. \n", + "\n", "### We concatenate the design matrix by 2 times, mimicking 2 runs of identical timing" ] }, @@ -394,7 +395,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Fit Bayesian RSA to our simulated data" + "# Fit Bayesian RSA to our simulated data\n", + "n_nureg tells the model how many principal components to keep from the residual as nuisance regressors in order to account for spatial correlation in noise.\n", + "The nuisance regressors in typical fMRI analysis (such as head motion signal) are replaced by principal components estimated from residuals after subtracting task-related response. If you prefer not using this approach based on principal components of residuals, you can set auto_nuisance=False, and optionally provide your own nuisance regressors" ] }, { @@ -406,11 +409,12 @@ "outputs": [], "source": [ "brsa = BRSA(GP_space=True, GP_inten=True,\n", - " tau_range=10, n_nureg=10)\n", + " n_nureg=10)\n", "# Initiate an instance, telling it\n", "# that we want to impose Gaussian Process prior\n", "# over both space and intensity.\n", "\n", + "\n", "brsa.fit(X=Y, design=design.design_task,\n", " coords=coords_flat, inten=inten, scan_onsets=scan_onsets)\n", "# The data to fit should be given to the argument X.\n", From 08e1d5cd56c071641ebb9d7e0dde21c9da7ab7b6 Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 23 Oct 2016 21:41:12 -0400 Subject: [PATCH 24/30] updating example to do z-scoring --- brainiak/reprsimil/brsa.py | 152 +++++++++++------- ...tational_similarity_estimate_example.ipynb | 81 +++++----- tests/reprsimil/test_brsa.py | 20 +-- 3 files changed, 145 insertions(+), 108 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 70d7e0ebf..109bcb3e6 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -506,7 +506,7 @@ def _prepare_data_XYX0(self, X, Y, X0, D, F, run_TRs, no_DC=False): # If a set of regressors for non-interested signals is not # provided, then we simply include one baseline for each run. X0 = X_base - logger.info('You did not provide time seres of no interest ' + logger.info('You did not provide time series of no interest ' 'such as DC component. One trivial regressor of' ' DC component is included for further modeling.' ' The final covariance matrix won''t ' @@ -593,7 +593,32 @@ def _calc_LL(self, rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, SNR2, # in addition to a few other terms. LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank + # try: LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) + # except: +# m_rank = np.empty(n_V) +# for i in range(n_V): +# m_rank[i] = np.linalg.matrix_rank(LAMBDA_i[i]) +# idx = np.where(m_rank < rank) +# print('lower ranks {}'.format(idx)) +# print('SNR2 at lower rank voxel: {}'.format(SNR2[idx])) +# print('LAMBDA_i at lower rank voxel: {}'.format(LAMBDA_i[idx])) +# idx = np.where(np.logical_not(np.isfinite(SNR2))) +# print('bad SNR2 index {}'.format(idx)) +# print('bad values in SNR2: {}'.format( +# SNR2[idx])) +# print('corresponding LAMBDA_i: {}'.format( +# LAMBDA_i[idx, :, :])) +# idx = np.where(SNR2 == 0) +# print('bad SNR2 index {}'.format(idx)) +# print('bad values in SNR2: {}'.format( +# SNR2[idx])) +# print('corresponding LAMBDA_i: {}'.format( +# LAMBDA_i[idx, :, :])) +# print('LTXTAcorrXL: {}'.format(LTXTAcorrXL)) +# print('bad values in rho1: {}.'.format( +# rho1[np.where(np.abs(rho1) == 1)])) +# raise # dimension: space*rank*rank # LAMBDA is essentially the inverse covariance matrix of the # posterior probability of alpha, which bears the relation with @@ -1011,6 +1036,29 @@ def _fit_diagV_noGP( X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( X, Y, X0, D, F, run_TRs, no_DC=True) + + # fit U, the covariance matrix, together with AR(1) param + param0_fitU[idx_param_fitU['Cholesky']] = \ + current_vec_U_chlsk_l + param0_fitU[idx_param_fitU['a1']] = current_a1 + res_fitU = scipy.optimize.minimize( + self._loglike_AR1_diagV_fitU, param0_fitU, + args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_logSNR2, l_idx, n_C, + n_T, n_V, n_run, n_base, idx_param_fitU, rank), + method=self.optimizer, jac=True, tol=tol, + options={'xtol': tol, 'disp': self.verbose, + 'maxiter': 4}) + current_vec_U_chlsk_l = \ + res_fitU.x[idx_param_fitU['Cholesky']] + current_a1 = res_fitU.x[idx_param_fitU['a1']] + norm_fitUchange = np.linalg.norm(res_fitU.x - param0_fitU) + logger.debug('norm of parameter change after fitting U: ' + '{}'.format(norm_fitUchange)) + param0_fitU = res_fitU.x.copy() + # fit V, reflected in the log(SNR^2) of each voxel rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l @@ -1043,7 +1091,8 @@ def _fit_diagV_noGP( norm_fitVchange = np.linalg.norm(res_fitV.x - param0_fitV) logger.debug('norm of parameter change after fitting V: ' '{}'.format(norm_fitVchange)) - logger.debug('E[log(SNR2)^2]:'.format(np.mean(current_logSNR2**2))) + logger.debug('E[log(SNR2)^2]: {}'.format( + np.mean(current_logSNR2**2))) # The lines below are for debugging purpose. # If any voxel's log(SNR^2) gets to non-finite number, @@ -1057,28 +1106,6 @@ def _fit_diagV_noGP( param0_fitV = res_fitV.x.copy() - # fit U, the covariance matrix, together with AR(1) param - param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l - param0_fitU[idx_param_fitU['a1']] = current_a1 - res_fitU = scipy.optimize.minimize( - self._loglike_AR1_diagV_fitU, param0_fitU, - args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_logSNR2, l_idx, n_C, - n_T, n_V, n_run, n_base, idx_param_fitU, rank), - method=self.optimizer, jac=True, tol=tol, - options={'xtol': tol, 'disp': self.verbose, - 'maxiter': 3}) - current_vec_U_chlsk_l = \ - res_fitU.x[idx_param_fitU['Cholesky']] - current_a1 = res_fitU.x[idx_param_fitU['a1']] - norm_fitUchange = np.linalg.norm(res_fitU.x - param0_fitU) - logger.debug('norm of parameter change after fitting U: ' - '{}'.format(norm_fitUchange)) - param0_fitU = res_fitU.x.copy() - # Re-estimating X0 from residuals current_SNR2 = np.exp(current_logSNR2) if self.auto_nuisance: @@ -1135,6 +1162,33 @@ def _fit_diagV_GP( X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \ X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( X, Y, X0, D, F, run_TRs, no_DC=True) + # fit U + + param0_fitU[idx_param_fitU['Cholesky']] = \ + current_vec_U_chlsk_l + param0_fitU[idx_param_fitU['a1']] = current_a1 + + res_fitU = scipy.optimize.minimize( + self._loglike_AR1_diagV_fitU, param0_fitU, + args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, + XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, + XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, + current_logSNR2, l_idx, n_C, n_T, n_V, + n_run, n_base, idx_param_fitU, rank), + method=self.optimizer, jac=True, + tol=tol, + options={'xtol': tol, + 'disp': self.verbose, 'maxiter': 6}) + current_vec_U_chlsk_l = \ + res_fitU.x[idx_param_fitU['Cholesky']] + current_a1 = res_fitU.x[idx_param_fitU['a1']] + L[l_idx] = current_vec_U_chlsk_l + fitUchange = res_fitU.x - param0_fitU + norm_fitUchange = np.linalg.norm(fitUchange) + logger.debug('norm of parameter change after fitting U: ' + '{}'.format(norm_fitUchange)) + param0_fitU = res_fitU.x.copy() + # fit V rho1 = np.arctan(current_a1) * 2 / np.pi X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ @@ -1176,33 +1230,6 @@ def _fit_diagV_GP( logger.debug('E[log(SNR2)^2]: {}'.format( np.mean(current_logSNR2**2))) - # fit U - - param0_fitU[idx_param_fitU['Cholesky']] = \ - current_vec_U_chlsk_l - param0_fitU[idx_param_fitU['a1']] = current_a1 - - res_fitU = scipy.optimize.minimize( - self._loglike_AR1_diagV_fitU, param0_fitU, - args=(XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, - XTY, XTDY, XTFY, X0TX0, X0TDX0, X0TFX0, - XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, - current_logSNR2, l_idx, n_C, n_T, n_V, - n_run, n_base, idx_param_fitU, rank), - method=self.optimizer, jac=True, - tol=tol, - options={'xtol': tol, - 'disp': self.verbose, 'maxiter': 6}) - current_vec_U_chlsk_l = \ - res_fitU.x[idx_param_fitU['Cholesky']] - current_a1 = res_fitU.x[idx_param_fitU['a1']] - L[l_idx] = current_vec_U_chlsk_l - fitUchange = res_fitU.x - param0_fitU - norm_fitUchange = np.linalg.norm(fitUchange) - logger.debug('norm of parameter change after fitting U: ' - '{}'.format(norm_fitUchange)) - param0_fitU = res_fitU.x.copy() - # Re-estimating X0 from residuals current_SNR2 = np.exp(current_logSNR2) if self.auto_nuisance: @@ -1212,7 +1239,7 @@ def _fit_diagV_GP( n_V, n_T, n_run, rank, n_base) betas = current_sigma2**0.5 * current_SNR2 \ * np.dot(L, YTAcorrXL_LAMBDA.T) - residuals = Y - np.dot(X, betas) + residuals = Y[:, :-1] - np.dot(X, betas[:, :-1]) u, s, v = np.linalg.svd(residuals) X0 = u[:, :self.n_nureg] @@ -1291,16 +1318,21 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, L, rho1, n_V, n_base) # Only starting from this point, SNR2 is involved - LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ - = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, - SNR2, n_V, n_T, n_run, rank, n_base) + try: + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, + SNR2, n_V, n_T, n_run, rank, n_base) + except: + logger.debug('L: {}'.format(L)) + raise if not np.isfinite(LL): logger.debug('NaN detected!') - logger.debug(sigma2) - logger.debug(YTAcorrY) - logger.debug(LTXTAcorrY) - logger.debug(YTAcorrXL_LAMBDA) - logger.debug(SNR2) + logger.debug('LL: {}'.format(LL)) + logger.debug('sigma2: {}'.format(sigma2)) + logger.debug('YTAcorrY: {}'.format(YTAcorrY)) + logger.debug('LTXTAcorrY: {}'.format(LTXTAcorrY)) + logger.debug('YTAcorrXL_LAMBDA: {}'.format(YTAcorrXL_LAMBDA)) + logger.debug('SNR2: {}'.format(SNR2)) YTAcorrXL_LAMBDA_LT = np.dot(YTAcorrXL_LAMBDA, L.T) # dimension: space*feature (feature can be larger than rank) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 8ea25bd4c..31dfcba8e 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -7,7 +7,7 @@ }, "source": [ "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset.\n", - "Questions can be directed to mcai [ at ] princeton [ dot ] edu" + "*Feedbacks and questions are welcome. Please direct them to mcai [ at ] princeton [ dot ] edu" ] }, { @@ -342,6 +342,14 @@ "# The data to be fed to the program.\n", "\n", "\n", + "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", + "plt.pcolor(np.reshape(snr, [ROI_edge, ROI_edge]))\n", + "plt.colorbar()\n", + "ax = plt.gca()\n", + "ax.set_aspect(1)\n", + "plt.title('pseudo-SNR in a square \"ROI\"')\n", + "plt.show()\n", + "\n", "idx = np.argmin(np.abs(snr - np.median(snr)))\n", "# choose a voxel of medium level SNR.\n", "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", @@ -357,24 +365,35 @@ "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", " facecolor='w', edgecolor='k')\n", "data_plot, = plt.plot(Y[:,idx],'b')\n", - "plt.legend([data_plot], ['observed data'])\n", + "plt.legend([data_plot], ['observed data of the voxel'])\n", "plt.xlabel('time')\n", "plt.show()\n", "\n", - "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(np.reshape(snr, [ROI_edge, ROI_edge]))\n", - "plt.colorbar()\n", - "ax = plt.gca()\n", - "ax.set_aspect(1)\n", - "plt.title('pseudo-SNR in a square \"ROI\"')\n", - "plt.show()" + "idx = np.argmin(np.abs(snr - np.max(snr)))\n", + "# display the voxel of the highest level SNR.\n", + "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", + "noise_plot, = plt.plot(noise[:,idx],'g')\n", + "signal_plot, = plt.plot(signal[:,idx],'r')\n", + "plt.legend([noise_plot, signal_plot], ['noise', 'signal'])\n", + "plt.title('simulated data in the voxel with the highest'\n", + " ' pseudo-SNR of {}'.format(snr[idx]))\n", + "plt.xlabel('time')\n", + "plt.show()\n", + "\n", + "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", + " facecolor='w', edgecolor='k')\n", + "data_plot, = plt.plot(Y[:,idx],'b')\n", + "plt.legend([data_plot], ['observed data of the voxel'])\n", + "plt.xlabel('time')\n", + "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "#### The reason that the pseudo-SNR in the example voxel is not too small, while the signal looks much smaller is because we happen to have low amplitudes in our design matrix. The true SNR depends on both the amplitudes in design matrix and the pseudo-SNR. Therefore, be aware that pseudo-SNR does not directly reflects how much signal the data have, but rather a map indicating the relative strength of signal in differerent voxels.\n", + "#### The reason that the pseudo-SNRs in the example voxels are not too small, while the signal looks much smaller is because we happen to have low amplitudes in our design matrix. The true SNR depends on both the amplitudes in design matrix and the pseudo-SNR. Therefore, be aware that pseudo-SNR does not directly reflects how much signal the data have, but rather a map indicating the relative strength of signal in differerent voxels.\n", "#### When you have multiple runs, the noise won't be correlated between runs. Therefore, you should tell BRSA when is the onset of each scan. \n", "#### Note that the data (variable Y above) you feed to BRSA is the concatenation of data from all runs along the time dimension, as a 2-D matrix of time x space" ] @@ -396,8 +415,10 @@ "metadata": {}, "source": [ "# Fit Bayesian RSA to our simulated data\n", - "n_nureg tells the model how many principal components to keep from the residual as nuisance regressors in order to account for spatial correlation in noise.\n", - "The nuisance regressors in typical fMRI analysis (such as head motion signal) are replaced by principal components estimated from residuals after subtracting task-related response. If you prefer not using this approach based on principal components of residuals, you can set auto_nuisance=False, and optionally provide your own nuisance regressors" + "### The data should be z-scored along time dimension. Otherwise voxels of high variance in noise can dominate the estimation of spatially shared noise component.\n", + "\n", + "The nuisance regressors in typical fMRI analysis (such as head motion signal) are replaced by principal components estimated from residuals after subtracting task-related response. n_nureg tells the model how many principal components to keep from the residual as nuisance regressors, in order to account for spatial correlation in noise. \n", + "If you prefer not using this approach based on principal components of residuals, you can set auto_nuisance=False, and optionally provide your own nuisance regressors as nuisance argument to BRSA.fit()" ] }, { @@ -408,6 +429,10 @@ }, "outputs": [], "source": [ + "Y_z = scipy.stats.zscore(Y,axis=0)\n", + "Y_std = np.std(Y,axis=0)\n", + "# Z-scoreing the data\n", + "\n", "brsa = BRSA(GP_space=True, GP_inten=True,\n", " n_nureg=10)\n", "# Initiate an instance, telling it\n", @@ -415,7 +440,7 @@ "# over both space and intensity.\n", "\n", "\n", - "brsa.fit(X=Y, design=design.design_task,\n", + "brsa.fit(X=Y_z, design=design.design_task,\n", " coords=coords_flat, inten=inten, scan_onsets=scan_onsets)\n", "# The data to fit should be given to the argument X.\n", "# Design matrix goes to design. And so on.\n" @@ -477,7 +502,7 @@ "source": [ "regressor = np.insert(design.design_task,\n", " 0, 1, axis=1)\n", - "betas_point = np.linalg.lstsq(regressor, Y)[0]\n", + "betas_point = np.linalg.lstsq(regressor, Y_z)[0]\n", "point_corr = np.corrcoef(betas_point[1:, :])\n", "point_cov = np.cov(betas_point[1:, :])\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", @@ -578,14 +603,6 @@ }, "outputs": [], "source": [ - "plt.scatter(noise_level * np.sqrt(0.1/1.1), brsa.sigma_)\n", - "plt.xlabel('true \"independent\" noise level')\n", - "plt.ylabel('recovered \"independent\" noise level')\n", - "ax = plt.gca()\n", - "ax.set_aspect(1)\n", - "ax.set_xticks(np.arange(0.1,0.7,0.1))\n", - "ax.set_yticks(np.arange(0.1,0.7,0.1))\n", - "plt.show()\n", "\n", "plt.scatter(rho1, brsa.rho_)\n", "plt.xlabel('true AR(1) coefficients')\n", @@ -619,19 +636,17 @@ }, "outputs": [], "source": [ - "plt.scatter(betas_simulated, brsa.beta_)\n", + "plt.scatter(betas_simulated / Y_std, brsa.beta_)\n", "plt.xlabel('true betas (response amplitudes)')\n", "plt.ylabel('recovered betas by Bayesian RSA')\n", "ax = plt.gca()\n", - "ax.set_aspect(1)\n", "plt.show()\n", "\n", "\n", - "plt.scatter(betas_simulated, betas_point[1:, :])\n", + "plt.scatter(betas_simulated / Y_std, betas_point[1:, :])\n", "plt.xlabel('true betas (response amplitudes)')\n", "plt.ylabel('recovered betas by simple regression')\n", "ax = plt.gca()\n", - "ax.set_aspect(1)\n", "plt.show()" ] }, @@ -651,7 +666,7 @@ }, "outputs": [], "source": [ - "u, s, v = np.linalg.svd(noise)\n", + "u, s, v = np.linalg.svd(Y_z - signal / Y_std)\n", "plt.plot(s)\n", "plt.xlabel('principal component')\n", "plt.ylabel('singular value of simulated noise')\n", @@ -664,18 +679,8 @@ "\n", "plt.pcolor(np.reshape(brsa.beta0_[0,:], [ROI_edge, ROI_edge]))\n", "plt.title('Weights of the first recovered principal component in noise')\n", - "plt.show()\n", - "print(brsa.beta0_.shape)" + "plt.show()" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index cfb832434..681545216 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -336,7 +336,7 @@ def test_gradient(): l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing)[0], param0_sing, vec) - assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt Cholesky is incorrect' + assert np.isclose(dd, np.dot(deriv0, vec), rtol=1e-5), 'gradient of singpara wrt Cholesky is incorrect' # We test the gradient to a1 vec = np.zeros(np.size(param0_sing)) @@ -347,7 +347,7 @@ def test_gradient(): l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing)[0], param0_sing, vec) - assert np.isclose(dd, np.dot(deriv0, vec), rtol=0.01), 'gradient of singpara wrt a1 is incorrect' + assert np.isclose(dd, np.dot(deriv0, vec), rtol=1e-5), 'gradient of singpara wrt a1 is incorrect' # log likelihood and derivative of the fitU function. @@ -365,7 +365,7 @@ def test_gradient(): XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitU, n_C)[0], param0_fitU, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt to AR(1) coefficient incorrect' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitU wrt to AR(1) coefficient incorrect' # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct vec = np.zeros(np.size(param0_fitU)) @@ -375,7 +375,7 @@ def test_gradient(): XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run,n_base, idx_param_fitU, n_C)[0], param0_fitU, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitU wrt Cholesky factor incorrect' # Test on a random direction vec = np.random.randn(np.size(param0_fitU)) @@ -385,7 +385,7 @@ def test_gradient(): XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitU, n_C)[0], param0_fitU, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitU incorrect' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitU incorrect' # We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior. X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ @@ -420,7 +420,7 @@ def test_gradient(): l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitV, n_C, False, False)[0], param0_fitV[idx_param_fitV['log_SNR2']], vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitV wrt log(SNR2) incorrect for model without GP' # We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior. ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, X0TAX0, XTAX0, X0TAY, @@ -440,7 +440,7 @@ def test_gradient(): idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV srt log(SNR2) incorrect for model with GP' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitV srt log(SNR2) incorrect for model with GP' # We test the graident wrt spatial length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) @@ -453,7 +453,7 @@ def test_gradient(): idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt spatial length scale of GP incorrect' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitV wrt spatial length scale of GP incorrect' # We test the graident wrt intensity length scale parameter of GP prior vec = np.zeros(np.size(param0_fitV)) @@ -466,7 +466,7 @@ def test_gradient(): idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV wrt intensity length scale of GP incorrect' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitV wrt intensity length scale of GP incorrect' # We test the graident on a random direction vec = np.random.randn(np.size(param0_fitV)) @@ -479,4 +479,4 @@ def test_gradient(): idx_param_fitV, n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=0.01), 'gradient of fitV incorrect' + assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitV incorrect' From dbb55222e67463150b7001c0d668203ba97caf95 Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 23 Oct 2016 22:38:42 -0400 Subject: [PATCH 25/30] cleaning up --- brainiak/reprsimil/brsa.py | 30 +------ ...tational_similarity_estimate_example.ipynb | 87 ------------------- 2 files changed, 3 insertions(+), 114 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index cfad4cdb3..33465dca4 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -596,9 +596,7 @@ def _calc_LL(self, rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, SNR2, LAMBDA_i = LTXTAcorrXL * SNR2[:, None, None] + np.eye(rank) # dimension: space*rank*rank - LAMBDA = np.linalg.solve(LAMBDA_i, np.identity(rank)[None, :, :]) - # dimension: space*rank*rank # LAMBDA is essentially the inverse covariance matrix of the # posterior probability of alpha, which bears the relation with @@ -1017,7 +1015,6 @@ def _fit_diagV_noGP( X0TY, X0TDY, X0TFY, X0, n_base = self._prepare_data_XYX0( X, Y, X0, D, F, run_TRs, no_DC=True) - # fit U, the covariance matrix, together with AR(1) param param0_fitU[idx_param_fitU['Cholesky']] = \ current_vec_U_chlsk_l @@ -1040,8 +1037,6 @@ def _fit_diagV_noGP( '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() - - # fit V, reflected in the log(SNR^2) of each voxel rho1 = np.arctan(current_a1) * 2 / np.pi L[l_idx] = current_vec_U_chlsk_l @@ -1089,21 +1084,6 @@ def _fit_diagV_noGP( param0_fitV = res_fitV.x.copy() - - # Re-estimating X0 from residuals - current_SNR2 = np.exp(current_logSNR2) - if self.auto_nuisance: - LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, current_sigma2 \ - = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, - X0TAX0, current_SNR2, - n_V, n_T, n_run, rank, n_base) - betas = current_sigma2**0.5 * current_SNR2 \ - * np.dot(L, YTAcorrXL_LAMBDA.T) - residuals = Y - np.dot(X, betas) - u, s, v = np.linalg.svd(residuals) - X0 = u[:, :self.n_nureg] - - # Re-estimating X0 from residuals current_SNR2 = np.exp(current_logSNR2) if self.auto_nuisance: @@ -1113,7 +1093,7 @@ def _fit_diagV_noGP( n_V, n_T, n_run, rank, n_base) betas = current_sigma2**0.5 * current_SNR2 \ * np.dot(L, YTAcorrXL_LAMBDA.T) - residuals = Y - np.dot(X, betas) + residuals = Y[:, :-1] - np.dot(X, betas[:, :-1]) u, s, v = np.linalg.svd(residuals) X0 = u[:, :self.n_nureg] @@ -1188,8 +1168,6 @@ def _fit_diagV_GP( '{}'.format(norm_fitUchange)) param0_fitU = res_fitU.x.copy() - - # fit V rho1 = np.arctan(current_a1) * 2 / np.pi X0TAX0, XTAX0, X0TAY, X0TAX0_i, \ @@ -1322,8 +1300,8 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, try: LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ - = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, X0TAX0, - SNR2, n_V, n_T, n_run, rank, n_base) + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, SNR2, n_V, n_T, n_run, rank, n_base) except: logger.debug('L: {}'.format(L)) raise @@ -1336,8 +1314,6 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, logger.debug('YTAcorrXL_LAMBDA: {}'.format(YTAcorrXL_LAMBDA)) logger.debug('SNR2: {}'.format(SNR2)) - - YTAcorrXL_LAMBDA_LT = np.dot(YTAcorrXL_LAMBDA, L.T) # dimension: space*feature (feature can be larger than rank) deriv_L = -np.einsum('ijk,ikl,i', XTAcorrXL, LAMBDA, SNR2) \ diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 589db8bcd..2219053e2 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -7,11 +7,7 @@ }, "source": [ "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset.\n", - "*Feedbacks and questions are welcome. Please direct them to mcai [ at ] princeton [ dot ] edu" - - "Questions can be directed to mcai [ at ] princeton [ dot ] edu" - ] }, { @@ -156,11 +152,7 @@ "rho1_bot = -0.2\n", "rho1 = np.random.rand(n_V) \\\n", " * (rho1_top - rho1_bot) + rho1_bot\n", - "\n", - - - "noise_smooth_width = 10.0\n", "coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", "coords_flat = np.reshape(coords,[3, n_V]).T\n", @@ -354,7 +346,6 @@ "# The data to be fed to the program.\n", "\n", "\n", - "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", "plt.pcolor(np.reshape(snr, [ROI_edge, ROI_edge]))\n", "plt.colorbar()\n", @@ -363,8 +354,6 @@ "plt.title('pseudo-SNR in a square \"ROI\"')\n", "plt.show()\n", "\n", - - "idx = np.argmin(np.abs(snr - np.median(snr)))\n", "# choose a voxel of medium level SNR.\n", "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", @@ -384,7 +373,6 @@ "plt.xlabel('time')\n", "plt.show()\n", "\n", - "idx = np.argmin(np.abs(snr - np.max(snr)))\n", "# display the voxel of the highest level SNR.\n", "fig = plt.figure(num=None, figsize=(12, 4), dpi=150,\n", @@ -403,26 +391,13 @@ "plt.legend([data_plot], ['observed data of the voxel'])\n", "plt.xlabel('time')\n", "plt.show()\n" - - "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", - "plt.pcolor(np.reshape(snr, [ROI_edge, ROI_edge]))\n", - "plt.colorbar()\n", - "ax = plt.gca()\n", - "ax.set_aspect(1)\n", - "plt.title('pseudo-SNR in a square \"ROI\"')\n", - "plt.show()" - ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "#### The reason that the pseudo-SNRs in the example voxels are not too small, while the signal looks much smaller is because we happen to have low amplitudes in our design matrix. The true SNR depends on both the amplitudes in design matrix and the pseudo-SNR. Therefore, be aware that pseudo-SNR does not directly reflects how much signal the data have, but rather a map indicating the relative strength of signal in differerent voxels.\n", - - - "#### When you have multiple runs, the noise won't be correlated between runs. Therefore, you should tell BRSA when is the onset of each scan. \n", "#### Note that the data (variable Y above) you feed to BRSA is the concatenation of data from all runs along the time dimension, as a 2-D matrix of time x space" ] @@ -444,15 +419,10 @@ "metadata": {}, "source": [ "# Fit Bayesian RSA to our simulated data\n", - "### The data should be z-scored along time dimension. Otherwise voxels of high variance in noise can dominate the estimation of spatially shared noise component.\n", "\n", "The nuisance regressors in typical fMRI analysis (such as head motion signal) are replaced by principal components estimated from residuals after subtracting task-related response. n_nureg tells the model how many principal components to keep from the residual as nuisance regressors, in order to account for spatial correlation in noise. \n", "If you prefer not using this approach based on principal components of residuals, you can set auto_nuisance=False, and optionally provide your own nuisance regressors as nuisance argument to BRSA.fit()" -======= - "n_nureg tells the model how many principal components to keep from the residual as nuisance regressors in order to account for spatial correlation in noise.\n", - "The nuisance regressors in typical fMRI analysis (such as head motion signal) are replaced by principal components estimated from residuals after subtracting task-related response. If you prefer not using this approach based on principal components of residuals, you can set auto_nuisance=False, and optionally provide your own nuisance regressors" - ] }, { @@ -463,13 +433,10 @@ }, "outputs": [], "source": [ - "Y_z = scipy.stats.zscore(Y,axis=0)\n", "Y_std = np.std(Y,axis=0)\n", "# Z-scoreing the data\n", "\n", - - "brsa = BRSA(GP_space=True, GP_inten=True,\n", " n_nureg=10)\n", "# Initiate an instance, telling it\n", @@ -477,11 +444,7 @@ "# over both space and intensity.\n", "\n", "\n", - "brsa.fit(X=Y_z, design=design.design_task,\n", - - - " coords=coords_flat, inten=inten, scan_onsets=scan_onsets)\n", "# The data to fit should be given to the argument X.\n", "# Design matrix goes to design. And so on.\n" @@ -543,11 +506,7 @@ "source": [ "regressor = np.insert(design.design_task,\n", " 0, 1, axis=1)\n", - "betas_point = np.linalg.lstsq(regressor, Y_z)[0]\n", - - "betas_point = np.linalg.lstsq(regressor, Y)[0]\n", - "point_corr = np.corrcoef(betas_point[1:, :])\n", "point_cov = np.cov(betas_point[1:, :])\n", "fig = plt.figure(num=None, figsize=(4, 4), dpi=100)\n", @@ -648,17 +607,6 @@ }, "outputs": [], "source": [ - - - "plt.scatter(noise_level * np.sqrt(0.1/1.1), brsa.sigma_)\n", - "plt.xlabel('true \"independent\" noise level')\n", - "plt.ylabel('recovered \"independent\" noise level')\n", - "ax = plt.gca()\n", - "ax.set_aspect(1)\n", - "ax.set_xticks(np.arange(0.1,0.7,0.1))\n", - "ax.set_yticks(np.arange(0.1,0.7,0.1))\n", - "plt.show()\n", - "\n", "plt.scatter(rho1, brsa.rho_)\n", "plt.xlabel('true AR(1) coefficients')\n", @@ -692,7 +640,6 @@ }, "outputs": [], "source": [ - "plt.scatter(betas_simulated / Y_std, brsa.beta_)\n", "plt.xlabel('true betas (response amplitudes)')\n", "plt.ylabel('recovered betas by Bayesian RSA')\n", @@ -704,21 +651,6 @@ "plt.xlabel('true betas (response amplitudes)')\n", "plt.ylabel('recovered betas by simple regression')\n", "ax = plt.gca()\n", - - - - - - - - - - - - - - - "plt.show()" ] }, @@ -738,11 +670,7 @@ }, "outputs": [], "source": [ - "u, s, v = np.linalg.svd(Y_z - signal / Y_std)\n", - - - "plt.plot(s)\n", "plt.xlabel('principal component')\n", "plt.ylabel('singular value of simulated noise')\n", @@ -755,23 +683,8 @@ "\n", "plt.pcolor(np.reshape(brsa.beta0_[0,:], [ROI_edge, ROI_edge]))\n", "plt.title('Weights of the first recovered principal component in noise')\n", - "plt.show()" ] - - - - - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [] ->>>>>>> upstream/master } ], "metadata": { From 19b580af754dedb5bbf754721c33ee87f45395ad Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 23 Oct 2016 22:42:27 -0400 Subject: [PATCH 26/30] cleaning up --- brainiak/reprsimil/brsa.py | 4 ++-- tests/reprsimil/test_brsa.py | 2 -- 2 files changed, 2 insertions(+), 4 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 33465dca4..8e8be9643 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -1093,7 +1093,7 @@ def _fit_diagV_noGP( n_V, n_T, n_run, rank, n_base) betas = current_sigma2**0.5 * current_SNR2 \ * np.dot(L, YTAcorrXL_LAMBDA.T) - residuals = Y[:, :-1] - np.dot(X, betas[:, :-1]) + residuals = Y - np.dot(X, betas) u, s, v = np.linalg.svd(residuals) X0 = u[:, :self.n_nureg] @@ -1218,7 +1218,7 @@ def _fit_diagV_GP( n_V, n_T, n_run, rank, n_base) betas = current_sigma2**0.5 * current_SNR2 \ * np.dot(L, YTAcorrXL_LAMBDA.T) - residuals = Y[:, :-1] - np.dot(X, betas[:, :-1]) + residuals = Y - np.dot(X, betas) u, s, v = np.linalg.svd(residuals) X0 = u[:, :self.n_nureg] diff --git a/tests/reprsimil/test_brsa.py b/tests/reprsimil/test_brsa.py index a4f96dc58..ad25e2d53 100755 --- a/tests/reprsimil/test_brsa.py +++ b/tests/reprsimil/test_brsa.py @@ -347,7 +347,6 @@ def test_gradient(): l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_sing)[0], param0_sing, vec) - assert np.isclose(dd, np.dot(deriv0, vec), rtol=1e-5), 'gradient of singpara wrt a1 is incorrect' @@ -367,7 +366,6 @@ def test_gradient(): XTX0, XTDX0, XTFX0, X0TY, X0TDY, X0TFY, np.log(snr)*2, l_idx, n_C, n_T, n_V, n_run, n_base, idx_param_fitU, n_C)[0], param0_fitU, vec) - assert np.isclose(dd, np.dot(deriv0,vec), rtol=1e-5), 'gradient of fitU wrt to AR(1) coefficient incorrect' # We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct From 2ff981e00381af554c46fe5699e5f3a003742a3c Mon Sep 17 00:00:00 2001 From: lcnature Date: Mon, 24 Oct 2016 12:13:14 -0400 Subject: [PATCH 27/30] fix a bug in utils.ReadDesign --- brainiak/utils/utils.py | 2 +- ...sa_representational_similarity_estimate_example.ipynb | 9 ++------- 2 files changed, 3 insertions(+), 8 deletions(-) diff --git a/brainiak/utils/utils.py b/brainiak/utils/utils.py index a4e86d8e2..a159fd1fd 100644 --- a/brainiak/utils/utils.py +++ b/brainiak/utils/utils.py @@ -327,7 +327,7 @@ def read_afni(self, fname): int(split_by_at[1]) curr_idx += n_this_cond elif len(split_by_at) == 1 and \ - not re.search('..', split_by_at[0]): + not re.search('\..', split_by_at[0]): # Just a number, and not the type like '1..4' self.column_types[curr_idx] = int(split_by_at[0]) curr_idx += 1 diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 2219053e2..1ba4b99c0 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -158,11 +158,6 @@ "coords_flat = np.reshape(coords,[3, n_V]).T\n", "dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", "\n", - "noise_smooth_width = 10.0\n", - "coords = np.mgrid[0:ROI_edge, 0:ROI_edge, 0:1]\n", - "coords_flat = np.reshape(coords,[3, n_V]).T\n", - "dist2 = spdist.squareform(spdist.pdist(coords_flat, 'sqeuclidean'))\n", - "\n", "# generating noise\n", "K_noise = noise_level[:, np.newaxis] \\\n", " * (np.exp(-dist2 / noise_smooth_width**2 / 2.0) \\\n", @@ -690,7 +685,7 @@ "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -704,7 +699,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.2" + "version": "3.5.1" } }, "nbformat": 4, From de4a63b9af88e897dae3ff7ad2cccade033b31bd Mon Sep 17 00:00:00 2001 From: lcnature Date: Mon, 24 Oct 2016 12:18:17 -0400 Subject: [PATCH 28/30] bug fixing for BRSA._prepare_data_XYX0 --- brainiak/reprsimil/brsa.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index 8e8be9643..a731c1b89 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -497,7 +497,7 @@ def _prepare_data_XYX0(self, X, Y, X0, D, F, run_TRs, no_DC=False): if not np.any(np.isclose(res0[1], 0)): # No columns in X0 can be explained by the # baseline regressors. So we insert them. - X0 = np.concatenate(X_base, X0, axis=1) + X0 = np.concatenate((X_base, X0), axis=1) else: logger.warning('Provided regressors for non-interesting ' 'time series already include baseline. ' From 99645604aab7ed02a00f47c9b14007387544629e Mon Sep 17 00:00:00 2001 From: lcnature Date: Fri, 28 Oct 2016 13:19:53 -0400 Subject: [PATCH 29/30] trivial --- .../brsa_representational_similarity_estimate_example.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 1ba4b99c0..9e7f6428e 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -685,7 +685,7 @@ "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python 3", + "display_name": "Python [default]", "language": "python", "name": "python3" }, @@ -699,7 +699,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.1" + "version": "3.5.2" } }, "nbformat": 4, From 3d6172792aa2395b0b0e38637a7b716531bbd553 Mon Sep 17 00:00:00 2001 From: lcnature Date: Sun, 30 Oct 2016 11:19:46 -0400 Subject: [PATCH 30/30] changes re PR review --- brainiak/reprsimil/brsa.py | 26 +++++++------------ ...tational_similarity_estimate_example.ipynb | 3 +-- 2 files changed, 11 insertions(+), 18 deletions(-) diff --git a/brainiak/reprsimil/brsa.py b/brainiak/reprsimil/brsa.py index a731c1b89..6cec99e6f 100755 --- a/brainiak/reprsimil/brsa.py +++ b/brainiak/reprsimil/brsa.py @@ -506,9 +506,7 @@ def _prepare_data_XYX0(self, X, Y, X0, D, F, run_TRs, no_DC=False): # If a set of regressors for non-interested signals is not # provided, then we simply include one baseline for each run. X0 = X_base - logger.info('You did not provide time series of no interest ' - 'such as DC component. One trivial regressor of' ' DC component is included for further modeling.' ' The final covariance matrix won''t ' @@ -1298,21 +1296,17 @@ def _loglike_AR1_diagV_fitU(self, param, XTX, XTDX, XTFX, YTY_diag, # Only starting from this point, SNR2 is involved - try: - LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ - = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, - X0TAX0, SNR2, n_V, n_T, n_run, rank, n_base) - except: - logger.debug('L: {}'.format(L)) - raise + LL, LAMBDA_i, LAMBDA, YTAcorrXL_LAMBDA, sigma2 \ + = self._calc_LL(rho1, LTXTAcorrXL, LTXTAcorrY, YTAcorrY, + X0TAX0, SNR2, n_V, n_T, n_run, rank, n_base) if not np.isfinite(LL): - logger.debug('NaN detected!') - logger.debug('LL: {}'.format(LL)) - logger.debug('sigma2: {}'.format(sigma2)) - logger.debug('YTAcorrY: {}'.format(YTAcorrY)) - logger.debug('LTXTAcorrY: {}'.format(LTXTAcorrY)) - logger.debug('YTAcorrXL_LAMBDA: {}'.format(YTAcorrXL_LAMBDA)) - logger.debug('SNR2: {}'.format(SNR2)) + logger.warning('NaN detected!') + logger.warning('LL: {}'.format(LL)) + logger.warning('sigma2: {}'.format(sigma2)) + logger.warning('YTAcorrY: {}'.format(YTAcorrY)) + logger.warning('LTXTAcorrY: {}'.format(LTXTAcorrY)) + logger.warning('YTAcorrXL_LAMBDA: {}'.format(YTAcorrXL_LAMBDA)) + logger.warning('SNR2: {}'.format(SNR2)) YTAcorrXL_LAMBDA_LT = np.dot(YTAcorrXL_LAMBDA, L.T) # dimension: space*feature (feature can be larger than rank) diff --git a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb index 9e7f6428e..d7faea336 100644 --- a/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb +++ b/examples/reprsimil/brsa_representational_similarity_estimate_example.ipynb @@ -6,8 +6,7 @@ "collapsed": false }, "source": [ - "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset.\n", - "*Feedbacks and questions are welcome. Please direct them to mcai [ at ] princeton [ dot ] edu" + "# This demo shows how to use the Bayesian Representational Similarity Analysis method in brainiak with a simulated dataset." ] }, {