Abstract
Gene regulatory networks are a visual representation of genes and their interactions. In this visual representation, nodes correspond to genes, while edges correspond to interactions among genes. Learning the structure of a gene regulatory network from data can provide valuable insights on how genes regulate one another. Understanding the complex regulatory relationships among genes is key to understanding many biological processes. Methods that infer the structure of a gene regulatory network are powerful tools for understanding these processes. The inference from these methods has a wide range of applications such as understanding complex traits or diagnosing and treating disease. Probabilistic graphical models or networks describe the statistical dependence between variables in a system and graphical model based methods are commonly used to infer the structure of a gene regulatory network. We present a Bayesian graphical model based approach to infer the structure of a network and develop a Metropolis-Hastings algorithm for the inference. Our method quantifies uncertainty in the inference, uses edge-level prior probabilities, and incorporates prior or external knowledge of the network structure, and accounts for multiple data types (for example, discrete, continuous, and mixed). We illustrate the accuracy and efficiency of our method through simulation studies and compare our method to existing Bayesian methods. We demonstrate the practical application of our method by applying it to two different biological networks. First, we infer a gene regulatory network from individual level genotype and gene expression data in humans. Second, we infer the combinatorial binding profiles of transcription factors during Drosophila mesoderm development. We extend our method to infer gene regulatory networks by including biological assumptions that regulate the relationships between data types. Specifically, we use the principle of Mendelian randomization to infer causal relationships among genes by incorporating individual level genotype data in the network. We carry out a wide range of simulation studies on gene regulatory networks and demonstrate that our method can accurately infer regulatory relationships among genes.