Simultaneous Multiple Response Regression and Inverse Covariance Matrix Estimation via Penalized Gaussian Maximum Likelihood

• Activity Number: 561
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Wonyul Lee*+ and Yufeng Liu
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: Covariance estimation ; Joint estimation ; LASSO ; Multiple response ; Regression ; Sparsity

Abstract

Many multivariate regression techniques are designed for univariate response cases. For problems with multiple response variables available, one common approach is to apply the univariate response regression technique separately on each response variable. Although it is simple and popular, the univariate response approach ignores the information among response variables. In this paper, we propose two new methods for utilizing joint information among response variables. Both methods are in a penalized likelihood framework with weighted L1 regularization. The proposed methods provide sparse estimators of conditional inverse covariance matrix of response vector given explanatory variables as well as sparse estimators of regression parameters. Our first approach is to estimate the regression coefficients with plug-in estimated covariance matrices, and our second approach is to estimate the regression coefficients and the covariance matrix simultaneously. Asymptotic properties of our methods are explored. Through several simulated examples and application to a real Glioblastoma cancer data set, we demonstrate that the proposed methods perform competitively.