Skinny Gibbs: A Consistent and Scalable Gibbs Sampler for Model Selection

原文摘要

Naveen N. Narisettya, Juan Shenb* & Xuming Heca Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, ILb Department of Statistics, Fudan University, Shanghai, Chinac Department of Statistics, University of Michigan, Ann Arbor, MICONTACT Juan Shen shenjuan@fudan.edu.cn Department of Statistics, Fudan University, Shanghai, ChinaColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.UASA_A_1482754_Supplement.zipABSTRACTWe consider the computational and statistical issues for high-dimensional Bayesian model selection under the Gaussian spike and slab priors. To avoid large matrix computations needed in a standard Gibbs sampler, we propose a novel Gibbs sampler called “Skinny Gibbs” which is much more scalable to high-dimensional problems, both in memory and in computational efficiency. In particular, its computational complexity grows only linearly in p, the number of predictors, while retaining the property of strong model selection consistency even when p is much greater than the sample size n. The present article focuses on logistic regression due to its broad applicability as a representative member of the generalized linear models. We compare our proposed method with several leading variable selection methods through a simulation study to show that Skinny Gibbs has a strong performance as indicated by our theoretical work. Supplementary materials for this article are available online.

摘要来源：OpenAlex