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Goodness-of-fit Testing for Discrete Distributions via Stein Discrepancy
Jiasen Yang · Qiang Liu · Vinayak A Rao · Jennifer Neville

Thu Jul 12 09:15 AM -- 12:00 PM (PDT) @ Hall B #25

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.

Author Information

Jiasen Yang (Purdue University)
Qiang Liu (UT Austin)
Vinayak A Rao (Purdue University)
Jennifer Neville (Purdue University)

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