Gene networks are models of molecular interaction (such as gene-protein regulation, protein-protein interaction, and protein-metabolite association), and are used to explain many complex cellular functions affected by such interaction. Gene networks, in turn, help in formulating drug targets and, subsequently, drug design. This paper is targeted at the part of the bioinformatics research community that explores the interaction of genes for information flow.

The paper presents a Bayesian solution for the identification of such gene networks. The Bayesian solutions can be categorized as a point (hard) or probabilistic (soft) solution. The hard-point solution is conceptually simple, and has been the basis of many works in the field. However, it fails to provide a measure of confidence in the network topology that results. The soft probabilistic methods compute a posteriori probabilities (APP) of network topology, which is a measure of confidence in the network topology.

In the method proposed in this paper, the problem of gene interactions is formulated as a variable selection problem. An algorithm using a variational Bayesian expectation maximization (VBEM), which does not explicitly consider the uncertainty of the network topology, is proposed. This treatment can reduce the complexity of learning, and does not necessarily faithfully model the problem.

The paper presents a mathematical formulation of the problem, the VBEM solutions with constraints, and the proposed algorithm, in a brief summary. A brief treatment of the Bayesian integration of two data sets is also presented. This is followed by a test result for a simulated network with six regulators for yeast cell pathways. The test set the noise variance at .01, and collected results from 100 independent episodes. The algorithm has been reported to correctly infer most of the molecular interaction. When Bayesian data integration was used, additional interactions were inferred with a high degree of confidence. The proposed algorithms are claimed to outperform the Gibbs sampling algorithm. These claims, however, require further support.

The approach in this paper will be useful to researchers modeling complex, distributed, real-time industrial systems.