Joint Estimation of Multiple Graphical Models

• Activity Number: 112
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jian Guo*+ and Elizaveta Levina and George Michailidis and Ji Zhu
• Companies: University of Michigan and University of Michigan and University of Michigan and University of Michigan
• Keywords: Covariance matrix ; Graphical models ; Hierarchical penalty ; High-dimensional data ; Networks

Abstract

Gaussian graphical models explore dependence relationships between random variables. This paper develops an estimator for such models appropriate for heterogeneous data; specifically, data obtained from different categories that share some common structure, but also exhibit differences. We propose a method which jointly estimates several graphical models corresponding to the different categories. The method aims to preserve the common structure, while allowing for differences between the categories. This is achieved through a hierarchical penalty that targets the removal of common zeros in the precision matrices across categories. We establish the asymptotic theory for the proposed estimator, and illustrate its superior performance on a number of simulated networks. An application to learning semantic connections between terms from different types of webpages is also included.