Multiple Gaussian Graphical Models with Joint Sparsity and its Application to Pathway Enrichment Analysis
Hyonho Chun , Department of Statistics, Purdue University
Monday, October 3, 2011
4:00 p.m., room 223, Weber Bldg
Revealing networks of biological components is one of the key questions in systems biology and it has potential applications in understanding disease physiology and drug discovery - network medicine. With epitomized microarrays, we now measure multiple genes' expression simultaneously, and, thereby, we are able to statistically infer gene regulation networks from data. Gaussian graphical models (GGMs) have proven to be useful for this purpose, when gene expressions are measured from a single tissue/condition. However, in many recent studies, gene expressions have been measured from multiple tissues/conditions; therefore, in the present study, we employ an estimation procedure with GGMs with joint sparsity to increase the power of network inference. Our method is motivated by joint sparsity as a property of biological networks: The number of regulations is far less than that of a fully connected network, and this sparsity is preserved across multiple conditions. In order to impose joint sparsity, we use a class of nonconvex penalty functions. Our approach is capable of regularizing both common and condition-specific regularizations without explicit parametrization as well as has sparsistency in identifying regulations that do not occur under any condition. We show the performance of our approach by simulation and then apply it to pathway enrichment analysis with a gene expression dataset from the GenCord project, which reveals pathways that are enriched by active gene regulations in umbilical cord tissues.