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.
Natsuki KARIYA
Tokyo Institute of Technology
Sumio WATANABE
Tokyo Institute of Technology
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Natsuki KARIYA, Sumio WATANABE, "Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 11, pp. 1274-1282, November 2020, doi: 10.1587/transfun.2019EAP1172.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAP1172/_p
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@ARTICLE{e103-a_11_1274,
author={Natsuki KARIYA, Sumio WATANABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach},
year={2020},
volume={E103-A},
number={11},
pages={1274-1282},
abstract={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.},
keywords={},
doi={10.1587/transfun.2019EAP1172},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1274
EP - 1282
AU - Natsuki KARIYA
AU - Sumio WATANABE
PY - 2020
DO - 10.1587/transfun.2019EAP1172
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2020
AB - 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.
ER -