Bayesian Sparse Reduced Rank Multivariate Regression

• Activity Number: 305
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Gyuhyeong Goh* and Kun Chen and Dipak K. Dey
• Companies: University of Connecticut and University of Connecticut and University of Connecticut
• Keywords: Bayesian ; Low rank ; Penalized least squares ; Posterior consistency ; Sparsity

Abstract

Many modern statistical problems can be cast in the framework of multivariate regression, where the main task is the estimation of a possibly high-dimensional coefficient matrix. The low-rank structure in the coefficient matrix is of intrinsic multivariate nature, which, when further combined with sparsity, can further lift dimension reduction, conduct variable selection, and facilitate model interpretation. Using a Bayesian approach, we develop a unified sparse and low-rank multivariate regression method, to both estimate the coefficient matrix and obtain its credible region for making inference. The newly developed sparsity-inducing prior for the coefficient matrix enables simultaneous rank reduction, predictor selection, as well as response selection. We utilize the marginal likelihood to determine the regularization hyperparameter, so it maximizes its posterior probability given the data. Theoretically, the posterior consistency is established under a high-dimensional asymptotic regime.