Goodness-of-Fit Testing for Discrete Distributions via Stein Discrepancy
Jiasen Yang, Qiang Liu, Vinayak Rao, Jennifer Neville
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.
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.}
}