An empirical Bayes approach to network recovery using external knowledge

Reconstruction of a high-dimensional network may benefit substantially from the inclusion of prior knowledge on the network topology. In the case of gene interaction networks such knowledge may come for instance from pathway repositories like KEGG, or be inferred from data of a pilot study. The Bayesian framework provides a natural means of including such prior knowledge. Based on a Bayesian Simultaneous Equation Model, we develop an appealing Empirical Bayes (EB) procedure that automatically assesses the agreement of the used prior knowledge with the data at hand. We use variational Bayes method for posterior densities approximation and compare its accuracy with that of Gibbs sampling strategy. Our method is computationally fast, and can outperform known competitors. In a simulation study, we show that accurate prior data can greatly improve the reconstruction of the network, but need not harm the reconstruction if wrong. We demonstrate the benefits of the method in an analysis of gene expression data from GEO. In particular, the edges of the recovered network have superior reproducibility (compared to that of competitors) over resampled versions of the data.