Learning Directed Graphical Structures with Genetical Genomics Data

• Activity Number: 71
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Bin Gao*+ and Yuehua Cui
• Companies: Michigan State University and Michigan State University
• Keywords: Directed acyclic graphs ; Association analysis ; Gene network inference ; PC-algorithm ; Gene regulation

Abstract

Gene networks constructed with gene expressions often consider pairwise correlations between genes, thus may not reflect the true relationship between genes. Research has shown improved performance of inference on undirected graphical structure by considering possible genetic effects (Cai et al. 2013; Yin and Li 2011). Given that gene expressions are often due to directed regulations, we introduce a covariate-adjusted Gaussian graphical model to estimate the Markov equivalence class of the directed acyclic graphs (DAGs) in a genetical genomics analysis framework. We develop a two-step estimation procedure: 1) first estimate the regression coefficient matrix thus the means in our multi-response Gaussian model by a joint L1 penalization; 2) then use the residuals to estimate the regulatory networks of gene expression using PC-algorithm (Spirtes et al. 2000). The estimation consistency for high dimensional sparse DAGs is established. Simulations are conducted to demonstrate our theoretical results. We apply the method to an Alzheimer's disease dataset and show that our model can lead to an estimate closer to the real biological network than the model only considering gene expressions