Direct Estimation of the Difference of Two Precision Matrices

• Activity Number: 176
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Sihai Zhao*+ and Tony Cai and Hongzhe Li
• Companies: and University of Pennsylvania and University of Pennsylvania
• Keywords: Graphical model ; High-dimensional data ; Precision matrix

Abstract

In the analysis of genomic data we are often interested in how the structure of a genetic network may differ under two different conditions. Here we propose a method to directly recover the differential network, without separately estimating the condition-specific networks. In particular, we model the network in each condition using a Gaussian graphical model, whose structure corresponds to the sparsity pattern of the precision matrix of a multivariate normal random vector, and our method directly estimates the difference of two precision matrices. It is shown that under the assumption that the true differential network is sparse, our method outperforms separate estimation, and further we do not need to assume that the individual precision matrices are sparse. We show that our procedure is consistent in support recovery and estimation, and we illustrate these properties on simulated data as well as gene expression data from late-stage ovarian cancer patients.