  There has been an intense development on the estimation of a sparse
regression coefficient vector in statistics, machine learning and related
fields. In this paper, we focus on the Bayesian approach to this problem, where
sparsity is incorporated by the so-called spike-and-slab prior on the
coefficients. Instead of replying on MCMC for posterior inference, we propose a
fast and scalable algorithm based on variational approximation to the posterior
distribution. The updating scheme employed by our algorithm is different from
the one proposed by Carbonetto and Stephens (2012). Those changes seem crucial
for us to show that our algorithm can achieve asymptotic consistency even when
the feature dimension diverges exponentially fast with the sample size.
Empirical results have demonstrated the effectiveness and efficiency of the
proposed algorithm.
