Robust Bayesian inference of networks using Dirichlet t-distributions

TL;DR

This paper introduces a flexible Dirichlet t-distribution model for robust Bayesian network inference that handles multivariate data with outliers, balancing model complexity and computational efficiency.

Contribution

It proposes a novel Dirichlet process-based t-distribution model that interpolates between classical and alternative models, improving robustness and computational feasibility.

Findings

Enhanced robustness to outliers in multivariate data

Improved modeling of dependence structures

Balanced computational complexity

Abstract

Bayesian graphical modeling provides an appealing way to obtain uncertainty estimates when inferring network structures, and much recent progress has been made for Gaussian models. These models have been used extensively in applications to gene expression data, even in cases where there appears to be significant deviations from the Gaussian model. For more robust inferences, it is natural to consider extensions to t-distribution models. We argue that the classical multivariate t-distribution, defined using a single latent Gamma random variable to rescale a Gaussian random vector, is of little use in highly multivariate settings, and propose other, more flexible t-distributions. Using an independent Gamma-divisor for each component of the random vector defines what we term the alternative t-distribution. The associated model allows one to extract information from highly multivariate data even when most experiments contain outliers for some of their measurements. However, the use of this alternative model comes at increased computational cost and imposes constraints on the achievable correlation structures, raising the need for a compromise between the classical and alternative models. To this end we propose the use of Dirichlet processes for adaptive clustering of the latent Gamma-scalars, each of which may then divide a group of latent Gaussian variables. Dirichlet processes are commonly used to cluster independent observations; here they are used instead to cluster the dependent components of a single observation. The resulting Dirichlet t-distribution interpolates naturally between the two extreme cases of the classical and alternative t-distributions and combines more appealing modeling of the multivariate dependence structure with favorable computational properties.