Bayesian Variable Selection and Estimation for Group Lasso

TL;DR

This paper introduces a Bayesian approach using spike and slab priors for group lasso, demonstrating superior variable selection and estimation properties, including the oracle property, especially in bi-level selection scenarios.

Contribution

The paper develops a Bayesian sparse group selection method with spike and slab priors, improving variable selection and estimation accuracy over traditional methods.

Findings

Posterior median estimator has the oracle property under orthogonal designs.

Bayesian sparse group selection outperforms traditional methods in simulations.

The method effectively performs bi-level variable selection.

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.