Inferring regulatory networks using a hierarchical Bayesian graphical Gaussian model
In this paper, we propose a new formalism based on graphical Gaussian model (GGM) to infer genetic regulatory networks. A hierarchical Bayesian prior for the precision matrix of the GGM is introduced to impose a bias toward sparse graph structure. We show that the MAP estimation of the undirected graph can be readily obtained by a variant of the well-known Lasso regression algorithm. Then we integrate the estimated graph with the “CHIp-Chip” protein-binding location data to infer the regulatory networks using a post-processing algorithm. Compared to extant Bayesian network (BN) models for similar tasks, our formalism captures statistical dependencies among genes that are more prevalent and plausible in the biological system. Our approach is also capable of modeling partial correlations between mRNA levels and therefore goes beyond clustering-based approaches. We applied our method to an expression microarray data (more than 6000 genes) together with a genome-wide location analysis data (more than 100 TFs). Evaluated on the consistency with the GO annotations, our method achieves a significantly better performance than clustering and BN learning algorithms in discovering genetic regulatory modules.