Multiple Response Regression for Gaussian Mixture Models with Known Labels

• Activity Number: 285
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wonyul Lee*+ and Yufeng Liu and Wei Sun and David Neil Hayes and Ying Du
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: Covariance estimation ; LASSO ; Multiple response ; Sparsity ; Regression ; Hierarchical penalty

Abstract

Multiple response regression is a useful regression technique to model multiple response variables using the same set of predictor variables. Most existing methods for multiple response regression are designed for modeling homogeneous data. In many applications, however, one may have heterogeneous data where the samples are divided into multiple groups. In this paper, we consider modeling the data coming from a mixture of several Gaussian distributions with known group labels. A naive approach is to split the data into several groups according to the labels and model each group separately. Although it is simple, this approach ignores potential common structures across different groups. We propose new penalized methods to model all groups jointly in which the common and unique structures can be identified. The proposed methods estimate the regression coefficient matrix, as well as the conditional inverse covariance matrix of response variables. Asymptotic properties of the proposed methods are explored. An application to a glioblastoma cancer dataset reveals some interesting common and unique gene relationships across different cancer subtypes.