Maximum Regularized Likelihood Estimator of Finite Mixtures with a Structural Model

Abstract

This article discusses a problem in a finite mixture model. The likelihood inference often fails to offer proper performance in the situation where the finite mixture model is full without any structure such as in a normal mixture model with unspecified means and variances. Imposing a structural constraint on the full model can avoid the problem, but such a structural model may suffer from model inflexibility. In order to overcome this dilemma we propose a maximum regularized likelihood method with a penalty function defined by the Kullback–Leibler divergence from the distribution estimated in the structural model. Good performance of this method with the optimal selection of the penalty parameter by the cross-validatory criterion has been shown. As a specific interest we applied our method to the neurophysiological data analysis of evoked synaptic responses with amplitude fluctuations.

Keywords:

• Cross validation
• EM algorithm
• Infinite likelihood
• Mixture of distributions
• Model identification
• Regularized likelihood

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62H12

Acknowledgments

We thank Dr. Fumihito Saitoh for kindly providing his unpublished data of synaptic responses obtained from the rat cerebellum. This work is supported in part by grants from the Ministry of Education, Culture, Sports, Science and Technology.