Improved Inference of Gaussian Mixture Copula Model for Clustering and Reproducibility Analysis using Automatic Differentiation

TL;DR

This paper introduces AD-GMCM, a novel method using Automatic Differentiation to accurately estimate parameters of Gaussian Mixture Copula Models, improving clustering and reproducibility analysis over previous proxy-likelihood approaches.

Contribution

The paper presents a new AD-based approach for GMCM parameter estimation that guarantees convergence to the true likelihood, outperforming prior PEM methods.

Findings

AD-GMCM achieves more accurate parameter estimates.

Improved clustering and reproducibility analysis results.

Addresses degeneracy issues in GMCM unlike GMM.

Abstract

Copulas provide a modular parameterization of multivariate distributions that decouples the modeling of marginals from the dependencies between them. Gaussian Mixture Copula Model (GMCM) is a highly flexible copula that can model many kinds of multi-modal dependencies, as well as asymmetric and tail dependencies. They have been effectively used in clustering non-Gaussian data and in Reproducibility Analysis, a meta-analysis method designed to verify the reliability and consistency of multiple high-throughput experiments. Parameter estimation for GMCM is challenging due to its intractable likelihood. The best previous methods have maximized a proxy-likelihood through a Pseudo Expectation Maximization (PEM) algorithm. They have no guarantees of convergence or convergence to the correct parameters. In this paper, we use Automatic Differentiation (AD) tools to develop a method, called AD-GMCM, that can maximize the exact GMCM likelihood. In our simulation studies and experiments with real data, AD-GMCM finds more accurate parameter estimates than PEM and yields better performance in clustering and Reproducibility Analysis. We discuss the advantages of an AD-based approach, to address problems related to monotonic increase of likelihood and parameter identifiability in GMCM. We also analyze, for GMCM, two well-known cases of degeneracy of maximum likelihood in GMM that can lead to spurious clustering solutions. Our analysis shows that, unlike GMM, GMCM is not affected in one of the cases.