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June 2011 A majorization–minimization approach to variable selection using spike and slab priors
Tso-Jung Yen
Ann. Statist. 39(3): 1748-1775 (June 2011). DOI: 10.1214/11-AOS884

Abstract

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 l2 and l0 norms. A tight approximation to the l0 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.

Citation

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Tso-Jung Yen. "A majorization–minimization approach to variable selection using spike and slab priors." Ann. Statist. 39 (3) 1748 - 1775, June 2011. https://doi.org/10.1214/11-AOS884

Information

Published: June 2011
First available in Project Euclid: 25 July 2011

zbMATH: 1220.62065
MathSciNet: MR2850219
Digital Object Identifier: 10.1214/11-AOS884

Subjects:
Primary: 62H12
Secondary: 62F15 , 62J05

Keywords: Irrepresentable Condition , l_0 norm , majorization–minimization algorithms , MAP estimation

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • June 2011
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