On the properties of Gaussian Copula Mixture Models
This work addresses data analysis challenges for researchers and practitioners in statistics and machine learning, but it is incremental as it builds on existing GMM and copula methods.
The paper tackles the problem of modeling complex data distributions by extending Gaussian mixture models with copula concepts, resulting in improved goodness-of-fit compared to GMM using the same number of clusters.
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.