Spike and slab variational Bayes for high dimensional logistic regression

Understand

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.