Bayesian Sparse Group Selection

• Activity Number: 130
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ray-Bing Chen*+ and Chi-Hsiang Chu and Shinsheng Yuan and Ying Nian Wu
• Companies: National Cheng Kung University and National University of Kaohsiung and Academia Sinica and University of California, Los Angeles
• Keywords: Bayesian variable selection ; group-wise Gibbs sampler ; group sparsity ; median probability criterion

Abstract

This article proposes a Bayesian approach for the sparse group selection problem in regression models. In this problem, the variables or regressors are partitioned into different groups. In addition to group sparse assumption, it is further assumed that within each active group only a small number of variables are active. We adopt a Bayesian hierarchical formulation, where each candidate group is associated with a binary variable indicating whether the group is selected or not. Within each group, each candidate variable is also associated with a binary variable, indicating whether the variable is selected or not. In this Bayesian formulation, the sparse group selection problem can be solved by sampling from the posterior distribution of the two layers of indicator variables as well as the coefficients of the selected variables. We adopt a group-wise Gibbs sampler for posterior sampling. We demonstrate the proposed method by simulation studies as well as a real example. The simulation results show that the proposed method is competitive with the sparse group Lasso in terms of selecting the active groups as well as identifying the active variables within the selected groups.