Fix underdetermined regularized least squares#45
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Summary
Root cause
The augmented least-squares system used an
N x Midentity matrix and paddedthe right-hand side with
Nrows, whereNis the number of equations andMis the number of coefficients. For underdetermined systems (
N < M), this leftsome coefficients unregularized and produced a solution that did not minimize
the documented ridge objective.
For example, with
A = [[1, 1]],b = [1], and regularization weight1, theexpected ridge solution is
[1/3, 1/3]; the previous implementation returnedapproximately
[0, 1].Impact
Underdetermined systems now solve the documented regularized least-squares
objective. Square and overdetermined systems retain the same mathematical
result.
Testing
python gnm/shape/run_all_tests.py— 278 passed, 2 skippedpylint gnm/shape/fitting_utils/regularized_least_squares.py gnm/shape/fitting_utils/regularized_least_squares_test.py