For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach
Natsuki KARIYA Sumio WATANABE
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2020/11/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Information Theory
hypothesis test, Bayesian statistics, variational inference, singular model, mixture model, likelihood ratio,
Full Text: PDF>>
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.