A Variational Inference method for Bayesian variable selection

Variable selection is a classic problem in statistics. In this paper, we consider a Bayes variable selection problem based on spike-and-slab prior with mixed normal distribution proposed by Ro\v{c}kov\'a and George (2014). Motivated by Ormerod and You(2017, 2022), we use the variational inference and collapsed variational inference method to solve the Bayesian problem instead of MCMC. Like Ormerod and You(2017, 2022), we also explain how the sparsity estimator is induced, and under certain mild assumptions, we also prove the consistent and asymptotic results.