Probabilistic Edge Inference of Gene Networks with Bayesian Markov Random Field Modelling

Abstract

Gaussian graphical models (GGMs), also known as Gaussian Markov random field (MRF) models, are commonly used for gene regulatory network construction. Most current approaches to estimating network structure via GGMs can be categorized into a binary decision that determines if an edge exists through penalized optimization and a probabilistic approach that incorporates graph uncertainty. Analyses in the first category usually adopt the perspective of variable (edge) selection without consideration of probabilistic interpretation. Methods in the second group, particularly the Bayesian approach, often quantify the uncertainty in the network structure with a stochastic measure on the precision matrix. Nevertheless, these methods overlook the existence probability of an edge and its strength related to the dependence between nodes. This study simultaneously investigates the existence and intensity of edges for network structure learning. We propose a method that combines the Bayesian MRF model and conditional autoregressive model for the relationship between gene nodes. This analysis can evaluate the relative strength of the edges and further prioritize the edges of interest. Simulations and a glioblastoma cancer study were carried out to assess the performance of our proposed models and compare it with existing methods. The proposed approach shows stable performance and may identify novel structures with biological insights.