Robust graphical modeling of gene networks using classical and alternative T-distributions

TL;DR

This paper proposes robust graphical modeling of gene networks using multivariate t-distributions, employing penalized likelihood and EM algorithms for efficient and scalable inference, improving robustness over Gaussian models.

Contribution

It introduces the use of multivariate t-distributions for robust graph inference and develops efficient EM-based algorithms, including variational approximations, for large-scale problems.

Findings

Demonstrates robustness of t-distribution models in gene network inference

Develops EM algorithms with approximation techniques for computational efficiency

Provides scalable methods suitable for large gene expression datasets

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 multivariate $t$-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 computationally efficient approach to model selection in the $t$-distribution case. We consider two versions of multivariate $t$-distributions, one of which requires the use of approximation techniques. For this distribution, we describe a Markov chain Monte Carlo EM algorithm based on a Gibbs sampler as well as a simple variational approximation that makes the resulting method feasible in large problems.