Probabilistic Graphical Modeling under Heterogeneity

Probabilistic graphical models are powerful and widely used tools to quantify, visualize and interpret dependencies in complex biological systems such as highthroughput genomics and proteomics. However, most existing graphical modeling methods assume homogeneity within and across samples which restricts their broad applicability to cases where sample-specific heterogeneity exists e.g. tumor heterogeneity. We propose a flexible Bayesian approach called Graphical Regression (GraphR) which (a) allows direct incorporation of intrinsic factors of sample heterogeneity at different scales through a regression-based formulation, (b) enables sparse network estimation at a sample-specific level, (c) allows identification and uncertainty quantification of potential effects of heterogeneity on network structures, and (d) is computationally efficient through the use of variational Bayes algorithms. We illustrate the comparative efficiency of GraphR against existing methods in terms of graph structure recovery and computational cost across multiple realistic simulation settings. We use GraphR to analyze four diverse multi-omics and spatial transcriptomics datasets to study inter- and intra-sample molecular networks and delineate biological discoveries that otherwise cannot be revealed by existing approaches. We have developed a GraphR R-package along with an accompanying Shiny App that provides comprehensive analysis and dynamic visualization functions.