Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach

Natsuki KARIYA  Sumio WATANABE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.11   pp.1274-1282
Publication Date: 2020/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1172
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
hypothesis test,  Bayesian statistics,  variational inference,  singular model,  mixture model,  likelihood ratio,  

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Summary: 
The test of homogeneity for normal mixtures has been used in various fields, but its theoretical understanding is limited because the parameter set for the null hypothesis corresponds to singular points in the parameter space. In this paper, we shed a light on this issue from a new perspective, variational Bayes, and offer a theory for testing homogeneity based on it. Conventional theory has not reveal the stochastic behavior of the variational free energy, which is necessary for constructing a hypothesis test, has remained unknown. We clarify it for the first time and construct a new test base on it. Numerical experiments show the validity of our results.