  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.
