Bayesian Subset Modeling for High-Dimensional Generalized Linear Models

• 成果类型: Article
• 署名作者: Liang, Faming; Song, Qifan; Yu, Kai
• 署名单位: Texas A&M University System; Texas A&M University College Station; National Institutes of Health (NIH) - USA; NIH National Cancer Institute (NCI); NIH National Cancer Institute- Division of Cancer Epidemiology & Genetics
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.761942
• 发表日期: 2013
• 页码: 589-606
• 关键词: variable-selection; stochastic-approximation; monte-carlo; DISCOVERY; regression; regularization; CONVERGENCE; Consistency; likelihood; search

摘要

This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online.