Bayesian estimation of dynamic weights in Gaussian mixture models

TL;DR

This paper introduces a Bayesian framework for dynamic Gaussian mixture models with time-varying weights, enabling better data feature capture and applications in clustering, change-point detection, and process control.

Contribution

It develops two novel Bayesian nonlinear dynamic methods for estimating polynomial weight functions, extending Gaussian mixture models to time-dependent scenarios.

Findings

Methods successfully model data features in simulations and real datasets.

Application to cancer genomic data detects chromosome aberrations.

Proposed approaches outperform traditional static models.

Abstract

This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by simulated and real datasets. It can be useful in studies such as clustering, change-point and process control. In order to estimate the mixture weight function, we propose two new Bayesian nonlinear dynamic approaches for polynomial models, that can be extended to other problems involving polynomial nonlinear dynamic models. One of the methods, called here component-wise Metropolis-Hastings, apply the Metropolis-Hastings algorithm to each local level component of the state equation. It is more general and can be used in any situation where the observation and state equations are nonlinearly connected. The other method tends to be faster, but is applied specifically to binary data (using the probit link function). The performance of these methods of estimation, in the context of the proposed dynamic Gaussian mixture model, is evaluated through simulated datasets. Also, an application to an array Comparative Genomic Hybridization (aCGH) dataset from glioblastoma cancer illustrates our proposal, highlighting the ability of the method to detect chromosome aberrations.