The Joint Graphical Lasso for Inverse Covariance Estimation Across Multiple Classes

• Activity Number: 129
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Patrick Danaher*+ and Pei Wang and Daniela Witten
• Companies: University of Washington and Fred Hutchinson Cancer Research Center and University of Washington
• Keywords: network estimation ; graphical model ; gene expression ; generalized gradient descent ; graphical lasso

Abstract

We consider the problem of estimating multiple related but distinct graphical models on the basis of a high-dimensional data set with observations that belong to distinct classes. A motivating example occurs in the analysis of gene expression data for tissue samples with and without cancer. In this case, we might wish to estimate separate gene expression networks for the normal tissue and the tumor tissue. We expect the two networks to be similar, and so more accurate estimation may be possible using a joint approach. We propose the Joint Graphical Lasso for this purpose. We borrow strength across the classes in order to estimate multiple graphical models that share appropriate characteristics, such as the locations or weights of nonzero edges. Our approach is based upon maximizing a penalized log likelihood. We employ fused lasso or group lasso penalties, and implement a very computationally efficient solution. In a simulation study we demonstrate that our proposed approach leads to more accurate estimation of networks and covariance structure than competing approaches. We further illustrate our proposal on a publicly-available lung cancer gene expression data set.