Learning Transcriptional Regulatory Relationships Using Sparse Graphical Models

Understanding the organization and function of transcriptional regulatory networks by analyzing high-throughput gene expression profiles is a key problem in computational biology. The challenges in this work are 1) the lack of complete knowledge of the regulatory relationship between the regulators and the associated genes, 2) the potential for spurious associations due to confounding factors, and 3) the number of parameters to learn is usually larger than the number of available microarray experiments. We present a sparse (L1 regularized) graphical model to address these challenges. Our model incorporates known transcription factors and introduces hidden variables to represent possible unknown transcription and confounding factors. The expression level of a gene is modeled as a linear combination of the expression levels of known transcription factors and hidden factors. Using gene expression data covering 39,296 oligonucleotide probes from 1109 human liver samples, we demonstrate that our model better predicts out-of-sample data than a model with no hidden variables. We also show that some of the gene sets associated with hidden variables are strongly correlated with Gene Ontology categories. The software including source code is available at http://grnl1.codeplex.com.