Title: Variational Bayes for high-dimensional linear regression with sparse priors
Authors: Kolyan Ray - Imperial College London (United Kingdom) [presenting]
Botond Szabo - Vrije Universiteit Amsterdam (Netherlands)
Abstract: A core problem in Bayesian statistics is approximating difficult-to-compute posterior distributions. In variational Bayes (VB), a method from machine learning, one approximates the posterior through optimization, which is typically faster than Markov chain Monte Carlo. We study a mean-field (i.e. factorizable) VB approximation to Bayesian model selection priors, including the popular spike-and-slab prior, in sparse high-dimensional linear regression. We establish convergence rates for this VB approach, studying conditions under which it provides good estimation. We also discuss computational issues and study the empirical performance of the algorithm.