A MAJORIZATION-MINIMIZATION APPROACH TO VARIABLE SELECTION USING SPIKE AND SLAB PRIORS

• 成果类型: Article
• 署名作者: Yen, Tso-Jung
• 署名单位: Academia Sinica - Taiwan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS884
• 发表日期: 2011
• 页码: 1748-1775
• 关键词: nonconcave penalized likelihood; Lasso; regression; regularization; CLASSIFICATION

摘要

We develop a method to carry out MAP estimation for a class of Bayesian regression models in which coefficients are assigned with Gaussian-based spike and slab priors. The objective function in the corresponding optimization problem has a Lagrangian form in that regression coefficients are regularized by a mixture of squared l(2) and l(0) norms. A tight approximation to the l(0) norm using majorization minimization techniques is derived, and a coordinate descent algorithm in conjunction with a soft-thresholding scheme is used in searching for the optimizer of the approximate objective. Simulation studies show that the proposed method can lead to more accurate variable selection than other benchmark methods. Theoretical results show that under regular conditions, sign consistency can be established, even when the Irrepresentable Condition is violated. Results on posterior model consistency and estimation consistency, and an extension to parameter estimation in the generalized linear models are provided.