Model Selection for Gaussian Mixture Models

TL;DR

This paper introduces a new penalized likelihood approach for selecting the number of components in Gaussian mixture models, ensuring statistical consistency and improving model estimation.

Contribution

It proposes a novel penalized likelihood method and a modified EM algorithm for consistent model selection and parameter estimation in Gaussian mixtures.

Findings

Method is statistically consistent in selecting the number of components.

Modified EM algorithm effectively estimates parameters and selects model complexity.

Simulation and real data demonstrate improved performance over existing methods.

Abstract

This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models. The proposed method is shown to be statistically consistent in determining of the number of components. A modified EM algorithm is developed to simultaneously select the number of components and to estimate the mixing weights, i.e. the mixing probabilities, and unknown parameters of Gaussian distributions. Simulations and a real data analysis are presented to illustrate the performance of the proposed method.