Quantile Graphical Models: Bayesian Approaches

TL;DR

This paper introduces a Bayesian quantile-based method for estimating graphical models that are robust to outliers and applicable to diverse distributions, with scalable algorithms demonstrated on cancer proteomics data.

Contribution

It presents a novel Bayesian quantile graphical model approach with variational Bayes for large datasets, overcoming Gaussian model limitations.

Findings

Robust graph estimation under non-Gaussian distributions.

Scalable variational Bayes algorithms developed.

Application to cancer proteomics data shows practical utility.

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. In this article, 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. Furthermore, we develop efficient variational Bayes approximations to scale the methods for large data sets. Our methods are applied to a novel cancer proteomics data dataset wherein multiple proteomic antibodies are simultaneously assessed on tumor samples using reverse-phase protein arrays (RPPA) technology.