Constructing gene networks using variational Bayesian variable selection.

We propose a Bayesian approach for constructing gene networks based on microarray data. Especially, we focus on Bayesian methods that can provide soft (probabilistic) information. This soft information is attractive not only for its ability to measure the level of confidence of the solution, but also because it can be used to realize Bayesian data integration, an extremely important task in gene network research. We propose a variable selection formulation of gene regulation and develop an inference solution based on a variational Bayesian expectation maximization (VBEM) learning rule. This solution has better performance and lower complexity than the popular Monte Carlo sampling techniques. In addition, we develop a method to incorporate the often needed constraints into the VBEM algorithm, making it much more suitable for common cases of small data size. To further illustrate the advantage of the VBEM algorithm, we demonstrate a Bayesian data integration scheme using the soft information obtained from the VBEM algorithm. The efficacy of the proposed VBEM algorithm and the corresponding Bayesian data integration scheme is evaluated on both simulated data and the yeast cell cycle microarray data sets.

Uncovering gene regulatory networks from time-series microarray data with variational Bayesian structural expectation maximization.

We investigate in this paper reverse engineering of gene regulatory networks from time-series microarray data. We apply dynamic Bayesian networks (DBNs) for modeling cell cycle regulations. In developing a network inference algorithm, we focus on soft solutions that can provide a posteriori probability (APP) of network topology. In particular, we propose a variational Bayesian structural expectation maximization algorithm that can learn the posterior distribution of the network model parameters and topology jointly. We also show how the obtained APPs of the network topology can be used in a Bayesian data integration strategy to integrate two different microarray data sets. The proposed VBSEM algorithm has been tested on yeast cell cycle data sets. To evaluate the confidence of the inferred networks, we apply a moving block bootstrap method. The inferred network is validated by comparing it to the KEGG pathway map.