Spike and slab variational Bayes for high dimensional logistic regression
This work addresses scalable Bayesian inference for sparse high-dimensional data, offering a theoretically grounded and efficient alternative to MCMC, though it is incremental as it builds on existing variational Bayes and spike and slab priors.
The paper tackles high-dimensional logistic regression with Bayesian model selection priors using a mean-field spike and slab variational Bayes approximation, achieving optimal minimax convergence rates in ℓ₂ and prediction loss for sparse truths, as confirmed by improved performance over common sparse VB methods in numerical studies.
Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional logistic regression. We provide non-asymptotic theoretical guarantees for the VB posterior in both $\ell_2$ and prediction loss for a sparse truth, giving optimal (minimax) convergence rates. Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices. We confirm the improved performance of our VB algorithm over common sparse VB approaches in a numerical study.