On the properties of Gaussian Copula Mixture Models

TL;DR

This paper introduces Gaussian copula mixture models (GCMM), extending Gaussian mixture models by incorporating copula concepts, and demonstrates their improved data fitting and ability to handle un-synchronized data.

Contribution

The paper defines GCMM mathematically, develops extended EM algorithms for parameter estimation, and shows improved fit and flexibility over traditional GMMs.

Findings

GCMM outperforms GMM in goodness-of-fit tests

GCMM can handle un-synchronized multi-dimensional data

Extended EM algorithms effectively estimate GCMM parameters

Abstract

This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of its likelihood function. Additionally, the paper proposes extended Expectation Maximum algorithms to estimate parameters for the mixture of copulas. The marginal distributions corresponding to each component are estimated separately using nonparametric statistical methods. In the experiment, GCMM demonstrates improved goodness-of-fitting compared to GMM when using the same number of clusters. Furthermore, GCMM has the ability to leverage un-synchronized data across dimensions for more comprehensive data analysis.