A Sparse Bayesian Learning Method for Structural Equation Model-Based Gene Regulatory Network Inference

Gene regulatory networks (GRNs) are underlying networks identified by interactive relationships between genes. Reconstructing GRNs from massive genetic data is important for understanding gene functions and biological mechanism, and can provide effective service for medical treatment and genetic research. A series of artificial intelligence based methods have been proposed to infer GRNs from both gene expression data and genetic perturbations. The accuracy of such algorithms can be better than those models that just consider gene expression data. A structural equation model (SEM), which provides a systematic framework integrating both types of gene data conveniently, is a commonly used model for GRN inference. Considering the sparsity of GRNs, in this paper, we develop a novel sparse Bayesian inference algorithm based on Normal-Equation-Gamma (NEG) type hierarchical prior (BaNEG) to infer GRNs modeled with SEMs more accurately. First, we reparameterize an SEM as a linear type model by integrating the endogenous and exogenous variables; Then, a Bayesian adaptive lasso with a three-level NEG prior is applied to deduce the corresponding posterior mode and estimate the parameters. Simulations on synthetic data are run to compare the performance of BaNEG to some state-of-the-art algorithms, the results demonstrate that the proposed algorithm visibly outperforms the others. What's more, BaNEG is applied to infer underlying GRNs from a real data set composed of 47 yeast genes from Saccharomyces cerevisiae to discover potential relationships between genes.