Goodness-of-Fit Testing for Discrete Distributions via Stein Discrepancy

Jiasen Yang, Qiang Liu, Vinayak Rao, Jennifer Neville
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5561-5570, 2018.

Abstract

Recent work has combined Stein’s method with reproducing kernel Hilbert space theory to develop nonparametric goodness-of-fit tests for un-normalized probability distributions. However, the currently available tests apply exclusively to distributions with smooth density functions. In this work, we introduce a kernelized Stein discrepancy measure for discrete spaces, and develop a nonparametric goodness-of-fit test for discrete distributions with intractable normalization constants. Furthermore, we propose a general characterization of Stein operators that encompasses both discrete and continuous distributions, providing a recipe for constructing new Stein operators. We apply the proposed goodness-of-fit test to three statistical models involving discrete distributions, and our experiments show that the proposed test typically outperforms a two-sample test based on the maximum mean discrepancy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-yang18c, title = {Goodness-of-Fit Testing for Discrete Distributions via Stein Discrepancy}, author = {Yang, Jiasen and Liu, Qiang and Rao, Vinayak and Neville, Jennifer}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {5561--5570}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/yang18c/yang18c.pdf}, url = {https://proceedings.mlr.press/v80/yang18c.html}, abstract = {Recent work has combined Stein’s method with reproducing kernel Hilbert space theory to develop nonparametric goodness-of-fit tests for un-normalized probability distributions. However, the currently available tests apply exclusively to distributions with smooth density functions. In this work, we introduce a kernelized Stein discrepancy measure for discrete spaces, and develop a nonparametric goodness-of-fit test for discrete distributions with intractable normalization constants. Furthermore, we propose a general characterization of Stein operators that encompasses both discrete and continuous distributions, providing a recipe for constructing new Stein operators. We apply the proposed goodness-of-fit test to three statistical models involving discrete distributions, and our experiments show that the proposed test typically outperforms a two-sample test based on the maximum mean discrepancy.} }
Endnote
%0 Conference Paper %T Goodness-of-Fit Testing for Discrete Distributions via Stein Discrepancy %A Jiasen Yang %A Qiang Liu %A Vinayak Rao %A Jennifer Neville %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-yang18c %I PMLR %P 5561--5570 %U https://proceedings.mlr.press/v80/yang18c.html %V 80 %X Recent work has combined Stein’s method with reproducing kernel Hilbert space theory to develop nonparametric goodness-of-fit tests for un-normalized probability distributions. However, the currently available tests apply exclusively to distributions with smooth density functions. In this work, we introduce a kernelized Stein discrepancy measure for discrete spaces, and develop a nonparametric goodness-of-fit test for discrete distributions with intractable normalization constants. Furthermore, we propose a general characterization of Stein operators that encompasses both discrete and continuous distributions, providing a recipe for constructing new Stein operators. We apply the proposed goodness-of-fit test to three statistical models involving discrete distributions, and our experiments show that the proposed test typically outperforms a two-sample test based on the maximum mean discrepancy.
APA
Yang, J., Liu, Q., Rao, V. & Neville, J.. (2018). Goodness-of-Fit Testing for Discrete Distributions via Stein Discrepancy. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:5561-5570 Available from https://proceedings.mlr.press/v80/yang18c.html.

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