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December 2015 Bayesian Variable Selection and Estimation for Group Lasso
Xiaofan Xu, Malay Ghosh
Bayesian Anal. 10(4): 909-936 (December 2015). DOI: 10.1214/14-BA929

Abstract

The paper revisits the Bayesian group lasso and uses spike and slab priors for group variable selection. In the process, the connection of our model with penalized regression is demonstrated, and the role of posterior median for thresholding is pointed out. We show that the posterior median estimator has the oracle property for group variable selection and estimation under orthogonal designs, while the group lasso has suboptimal asymptotic estimation rate when variable selection consistency is achieved. Next we consider bi-level selection problem and propose the Bayesian sparse group selection again with spike and slab priors to select variables both at the group level and also within a group. We demonstrate via simulation that the posterior median estimator of our spike and slab models has excellent performance for both variable selection and estimation.

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Xiaofan Xu. Malay Ghosh. "Bayesian Variable Selection and Estimation for Group Lasso." Bayesian Anal. 10 (4) 909 - 936, December 2015. https://doi.org/10.1214/14-BA929

Information

Published: December 2015
First available in Project Euclid: 4 February 2015

zbMATH: 1334.62132
MathSciNet: MR3432244
Digital Object Identifier: 10.1214/14-BA929

Rights: Copyright © 2015 International Society for Bayesian Analysis

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Vol.10 • No. 4 • December 2015
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