Inferring Graphical Models in Heterogeneous Populations

• Activity Number: 222
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Ali Shojaie* and Takumi Saegusa
• Companies: University of Washington and Fred Hutchinson Cancer Research Center
• Keywords: graphical models ; high dimension ; clustering ; heterogeneity ; penalized estiamtion

Abstract

When applying graphical models to study biological and social networks, observations are often drawn from heterogenous populations. However, existing methods for joint estimation of multiple graphical models assume that subpopulations all subpopulations have the same level of similarity with each other, which is unrealistic in many application settings. We introduce a general framework for inferring graphical models from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourages similarity among disparate, but related, subpopulations while allowing for differences among estimated networks. We also discuss an extension of this algorithm, which combines graphical model estimation with hierarchical clustering, to allow inference in settings where subpopulation memberships and similarities are unknown. We discuss efficient computation of parameters, using an ADMM algorithm, and establish norm and model selection consistency of the proposed estimator. Empirical results on estimation of genetic networks of multiple subtypes of breast cancer, as well as simulation experiments, show the advantages of the proposed method over existing approaches.