A0527
Title: Bayesian group variable selection via penalized credible region
Authors: Weichang Yu - University of Melbourne (Australia)
Khue-Dung Dang - University of Western Australia (Australia) [presenting]
Abstract: A Bayesian method is proposed for grouped variable selection in high-dimensional regression models. Most existing Bayesian methods are subjected to either high computation costs due to long MCMC runs or yield ambiguous variable selection results due to non-sparse solution output. The proposed method, GroupPenCr, is built upon the penalized credible region framework, which allows efficient computations of a sequence of sparse solutions via existing algorithms. The focus is on settings where the number of predictors grows with sample size n. For this problem, it is proposed to use global-local shrinkage priors and to perform GroupPenCr on the mean-field variational Bayes posterior instead. This allows avoiding the computational hassle of implementing MCMC on ultra-high-dimensional data. Furthermore, it is shown that this approach is also variable selection consistent. Through extensive simulations, it is shown that GroupPenCr can outperform common methods for Bayesian group variable selection.
