Group Spike and Slab Variational Bayes

TL;DR

The paper presents GSVB, a scalable variational inference method for group sparse regression that achieves state-of-the-art performance with theoretical guarantees and practical utility across various datasets.

Contribution

Introduction of GSVB, a fast variational Bayes algorithm for group sparse regression with proven contraction rates and extensive empirical validation.

Findings

GSVB outperforms existing methods in predictive accuracy.

GSVB provides reliable variable selection and uncertainty quantification.

The method is computationally efficient compared to MCMC.

Abstract

We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian, Binomial and Poisson. Theoretical guarantees for our proposed approach are provided by deriving contraction rates for the variational posterior in grouped linear regression. Through extensive numerical studies, we demonstrate that GSVB provides state-of-the-art performance, offering a computationally inexpensive substitute to MCMC, whilst performing comparably or better than existing MAP methods. Additionally, we analyze three real world datasets wherein we highlight the practical utility of our method, demonstrating that GSVB provides parsimonious models with excellent predictive performance, variable selection and uncertainty quantification.