Robust Graphical Modeling with t-Distributions

TL;DR

This paper proposes using multivariate t-distributions with penalized likelihood and EM algorithm for robust graphical modeling, especially in gene expression data, offering a computationally efficient alternative to Gaussian models.

Contribution

It introduces a robust graphical modeling approach using t-distributions, combining penalized likelihood and EM algorithm for effective model selection.

Findings

Robust inference with t-distributions improves over Gaussian models.

Penalized likelihood with EM algorithm is computationally efficient.

Applicable to gene expression network analysis.

Abstract

Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent progress includes the development of fitting methodology involving penalization of the likelihood function. In this paper we advocate the use of the multivariate t and related distributions for more robust inference of graphs. In particular, we demonstrate that penalized likelihood inference combined with an application of the EM algorithm provides a simple and computationally efficient approach to model selection in the t-distribution case.