Quantile Graphical Models: A Bayesian Approach

• Activity Number: 501 - Bayesian Penalized Likelihood Methods for Gaussian Graphical Models
• Type: Invited
• Date/Time: Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Nilabja Guha* and Veera Baladandayuthapani and Bani Mallick
• Companies: University of Massachusetts Lowell and University of Michigan and Texas A&M University

Abstract

Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices and they are generated under a multivariate normal joint distribution. However, they suffer from several shortcomings since they are based on Gaussian distribution assumptions. Here, we propose a Bayesian quantile based approach for sparse estimation of graphs. We demonstrate that the resulting graph estimation is robust to outliers and applicable under general distributional assumptions and provides neighborhood selection consistency under moderate assumptions on the true data generating mechanism. Furthermore, we develop efficient variational Bayes approximations to scale the methods for large data sets.