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

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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.

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