Bayesian Sparse Group Selection

Ray Bing Chen, Chi Hsiang Chu, Shinsheng Yuan, Ying Nian Wu

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This article proposes a Bayesian approach for the sparse group selection problem in the regression model. In this problem, the variables are partitioned into different groups. It is assumed that only a small number of groups are active for explaining the response variable, and 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 active or not. Within each group, each candidate variable is also associated with a binary indicator, too. Thus, the sparse group selection problem can be solved by sampling from the posterior distribution of the two layers of indicator variables. We adopt a group-wise Gibbs sampler for posterior sampling. We demonstrate the proposed method by simulation studies as well as real examples. The simulation results show that the proposed method performs better than the sparse group Lasso in terms of selecting the active groups as well as identifying the active variables within the selected groups. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)665-683
Number of pages19
JournalJournal of Computational and Graphical Statistics
Volume25
Issue number3
DOIs
Publication statusPublished - 2016 Jul 2

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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