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

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.

💡 Research Summary

The paper addresses a well‑known limitation of Graphical Gaussian Models (GGMs) when applied to high‑dimensional biological data: their sensitivity to outliers and heavy‑tailed noise. To obtain a more robust inference of gene‑network structure, the authors propose replacing the multivariate normal assumption with multivariate t‑distributions, which naturally accommodate heavier tails through a degrees‑of‑freedom parameter (ν).

Two variants of the multivariate t‑distribution are considered. The first, the classical formulation, treats each observation as a scale‑mixture of normals: X_i | τ_i ~ N(μ, Σ/τ_i) with τ_i ~ Gamma(ν/2, ν/2). Because the complete‑data log‑likelihood (including the latent scales τ_i) is tractable, an EM algorithm can be derived. In the E‑step the expected scales E