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

We 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 scal...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2019-07, Vol.114 (527), p.1205-1217
Main Authors: Narisetty, Naveen N., Shen, Juan, He, Xuming
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian computation
Computer simulation
Estimating techniques
Generalized linear models
Gibbs sampling
High-dimensional data
Linear analysis
Logistic regression
Property
Regression analysis
Scalable computation
Simulation
Statistical analysis
Statistical methods
Statistical models
Statistics
Variable selection
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Summary:We 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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2018.1482754