Title: A Log-Linear Graphical Model for Inferring Genetic Networks from High-Throughput Sequencing Data

Abstract: Gaussian graphical models are often used to infer gene networks based on microarray expression data. Many scientists, however, have begun using high-throughput sequencing technologies to measure gene expression. As the resulting high-dimensional count data consists of counts of sequencing reads for each gene, Gaussian graphical models are not optimal for modeling gene networks based on this discrete data. We develop a novel method for estimating high-dimensional Poisson graphical models, the Log-Linear Graphical Model, allowing us to infer networks based on high-throughput sequencing data. Our model assumes a pair-wise Markov property: conditional on all other variables, each variable is Poisson. We estimate our model locally via neighborhood selection by fitting 1-norm penalized log-linear models. Additionally, we develop a fast parallel algorithm, an approach we call the Poisson Graphical Lasso, permitting us to fit our graphical model to high-dimensional genomic data sets. In simulations, we illustrate the effectiveness of our methods for recovering network structure from count data. A case study on breast cancer microRNAs, a novel application of graphical models, finds known regulators of breast cancer genes and discovers novel microRNA clusters and hubs that are targets for future research.