Quantile Graphical Models: An Approximate Bayesian Approach

• Activity Number: 598
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Nilabja Guha and Bani K. Mallick*
• Companies: Texas A&M University and Texas A&M University
• Keywords: variable selection ; mean field approximation ; quantile regression

Abstract

Graphical models are ubiquitous tools to describe the interdependence between variables mea- sured 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 and linear assumptions. In this article, we propose a Bayesian quantile based approach for sparse estimation of graphs and estimate the posterior graph by mean field approximations. We demonstrate that the resulting graph estimation is robust to outliers and applicable under general distributional assumptions. We use efficient variational Bayes approximations to scale the methods for large data sets. Our methods are applied to a novel cancer proteomics data dataset where-in multiple proteomic antibodies are simultaneously assessed on tumor samples using reverse-phase protein arrays (RPPA) technology.