Non-asymptotic Performance Guarantees for Neural Estimation of f-Divergences

Sreejith Sreekumar, Zhengxin Zhang, Ziv Goldfeld
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3322-3330, 2021.

Abstract

Statistical distances (SDs), which quantify the dissimilarity between probability distributions, are central to machine learning and statistics. A modern method for estimating such distances from data relies on parametrizing a variational form by a neural network (NN) and optimizing it. These estimators are abundantly used in practice, but corresponding performance guarantees are partial and call for further exploration. In particular, there seems to be a fundamental tradeoff between the two sources of error involved: approximation and estimation. While the former needs the NN class to be rich and expressive, the latter relies on controlling complexity. This paper explores this tradeoff by means of non-asymptotic error bounds, focusing on three popular choices of SDs—Kullback-Leibler divergence, chi-squared divergence, and squared Hellinger distance. Our analysis relies on non-asymptotic function approximation theorems and tools from empirical process theory. Numerical results validating the theory are also provided.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-sreekumar21a, title = { Non-asymptotic Performance Guarantees for Neural Estimation of f-Divergences }, author = {Sreekumar, Sreejith and Zhang, Zhengxin and Goldfeld, Ziv}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3322--3330}, 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/sreekumar21a/sreekumar21a.pdf}, url = {https://proceedings.mlr.press/v130/sreekumar21a.html}, abstract = { Statistical distances (SDs), which quantify the dissimilarity between probability distributions, are central to machine learning and statistics. A modern method for estimating such distances from data relies on parametrizing a variational form by a neural network (NN) and optimizing it. These estimators are abundantly used in practice, but corresponding performance guarantees are partial and call for further exploration. In particular, there seems to be a fundamental tradeoff between the two sources of error involved: approximation and estimation. While the former needs the NN class to be rich and expressive, the latter relies on controlling complexity. This paper explores this tradeoff by means of non-asymptotic error bounds, focusing on three popular choices of SDs—Kullback-Leibler divergence, chi-squared divergence, and squared Hellinger distance. Our analysis relies on non-asymptotic function approximation theorems and tools from empirical process theory. Numerical results validating the theory are also provided. } }
Endnote
%0 Conference Paper %T Non-asymptotic Performance Guarantees for Neural Estimation of f-Divergences %A Sreejith Sreekumar %A Zhengxin Zhang %A Ziv Goldfeld %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-sreekumar21a %I PMLR %P 3322--3330 %U https://proceedings.mlr.press/v130/sreekumar21a.html %V 130 %X Statistical distances (SDs), which quantify the dissimilarity between probability distributions, are central to machine learning and statistics. A modern method for estimating such distances from data relies on parametrizing a variational form by a neural network (NN) and optimizing it. These estimators are abundantly used in practice, but corresponding performance guarantees are partial and call for further exploration. In particular, there seems to be a fundamental tradeoff between the two sources of error involved: approximation and estimation. While the former needs the NN class to be rich and expressive, the latter relies on controlling complexity. This paper explores this tradeoff by means of non-asymptotic error bounds, focusing on three popular choices of SDs—Kullback-Leibler divergence, chi-squared divergence, and squared Hellinger distance. Our analysis relies on non-asymptotic function approximation theorems and tools from empirical process theory. Numerical results validating the theory are also provided.
APA
Sreekumar, S., Zhang, Z. & Goldfeld, Z.. (2021). Non-asymptotic Performance Guarantees for Neural Estimation of f-Divergences . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3322-3330 Available from https://proceedings.mlr.press/v130/sreekumar21a.html.

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