Efficient Interpolation of Density Estimators

Paxton Turner, Jingbo Liu, Philippe Rigollet
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2503-2511, 2021.

Abstract

We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation scheme to give a computationally efficient construction that converts the original estimator to a new estimator that can be queried efficiently and has low space requirements, all without adversely deteriorating the original approximation quality. Our result gives a new statistical perspective on the problem of fast evaluation of kernel density estimators in the presence of underlying smoothness. As a corollary, we give a succinct derivation of a classical result of Kolmogorov—Tikhomirov on the metric entropy of Holder classes of smooth functions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-turner21a, title = { Efficient Interpolation of Density Estimators }, author = {Turner, Paxton and Liu, Jingbo and Rigollet, Philippe}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {2503--2511}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/turner21a/turner21a.pdf}, url = {https://proceedings.mlr.press/v130/turner21a.html}, abstract = { We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation scheme to give a computationally efficient construction that converts the original estimator to a new estimator that can be queried efficiently and has low space requirements, all without adversely deteriorating the original approximation quality. Our result gives a new statistical perspective on the problem of fast evaluation of kernel density estimators in the presence of underlying smoothness. As a corollary, we give a succinct derivation of a classical result of Kolmogorov—Tikhomirov on the metric entropy of Holder classes of smooth functions. } }
Endnote
%0 Conference Paper %T Efficient Interpolation of Density Estimators %A Paxton Turner %A Jingbo Liu %A Philippe Rigollet %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-turner21a %I PMLR %P 2503--2511 %U https://proceedings.mlr.press/v130/turner21a.html %V 130 %X We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation scheme to give a computationally efficient construction that converts the original estimator to a new estimator that can be queried efficiently and has low space requirements, all without adversely deteriorating the original approximation quality. Our result gives a new statistical perspective on the problem of fast evaluation of kernel density estimators in the presence of underlying smoothness. As a corollary, we give a succinct derivation of a classical result of Kolmogorov—Tikhomirov on the metric entropy of Holder classes of smooth functions.
APA
Turner, P., Liu, J. & Rigollet, P.. (2021). Efficient Interpolation of Density Estimators . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:2503-2511 Available from https://proceedings.mlr.press/v130/turner21a.html.

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