GIBBS POSTERIOR FOR VARIABLE SELECTION IN HIGH-DIMENSIONAL CLASSIFICATION AND DATA MINING

• 成果类型: Article
• 署名作者: Jiang, Wenxin; Tanner, Martin A.
• 署名单位: Northwestern University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS547
• 发表日期: 2008
• 页码: 2207-2231
• 关键词: logistic-regression; distributions; models; CHOICE

摘要

In the popular approach of Bayesian variable selection (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with I Gibbs posterior originating in statistical mechanics. The Gibbs posterior is constructed from a risk function of practical interest (Such as the classification error) and aims at minimizing a risk function without modeling the data probabilistically. This can improve the performance over the Usual Bayesian approach, which depends on a probability model which may be misspecified. Conditions will be provided to achieve good risk performance, even in the presence of high dimensionality, when the number of candidate variables K can be much larger than the sample size n. In addition, we develop a convenient Markov chain Monte Carlo algorithm to implement BVS with the Gibbs posterior.