A0343
Title: Scalable Bayesian inference on high-dimensional multivariate linear regression
Authors: Kyoungjae Lee - Sungkyunkwan University (Korea, South) [presenting]
Xuan Cao - University of Cincinnati (United States)
Abstract: Jointly estimating the regression coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression are considered. Scalable computation in this framework is often challenging for Bayesian methods, and thus, available approaches either adopted a generalized likelihood without guaranteeing the positive definiteness of the precision matrix or employed a maximization algorithm to target the posterior mode, which cannot handle uncertainty. Two Bayesian methods are proposed: an exact method and an approximate two-step method. An exact method is first proposed based on spike and slab priors for the coefficient matrix and DAG-Wishart prior to the error precision matrix. The complexity of the proposed algorithm is comparable to the state-of-the-art generalized likelihood-based Bayesian method. To further enhance scalability, a two-step approach is developed by ignoring the dependency structure among response variables. After estimating the coefficient matrix, the posterior of the error precision matrix is calculated based on the estimated errors. To justify the two-step approach, it is proven that (i) selection consistency and posterior convergence rates for the coefficient matrix and (ii) selection consistency for the directed acyclic graph (DAG) of errors. The practical performance of the proposed methods is demonstrated through synthetic and real data analysis.
