Variational Bayes from the Primitive Initial Point for Gaussian Mixture Estimation

Abstract

Gaussian mixture model (GMM) is one of the important models to approximate probability distributions. There are various methods for Gaussian mixture estimation such as the EM algorithm, sampling method, and the Bayes method. In this paper, we are concerned with the Gaussian mixture estimation problem using the variational Bayes (VB), which is an approximation of the Bayes method. In the VB, it is important to choose its initial values carefully since the objective function of the problem is multimodal. In this paper, we propose a method which employs primitive initial point (PIP) as an initial value of the VB and performs multi-directional search from the PIP. We present the motivation and rationale of our method and demonstrate its effectiveness through numerical experiments using real data sets.