Scalable Spike-and-Slab

Spike-and-slab priors are commonly used for Bayesian variable selection, due to their inter-pretability and favorable statistical properties. However, existing samplers for spike-and-slab posteriors incur prohibitive computational costs when the number of variables is large. In this article, we propose Scalable Spike-and-Slab ( S 3 ), a scalable Gibbs sampling implementation for high-dimensional Bayesian regression with the continuous spike-and-slab prior of George & McCulloch (1993). For a dataset with n observations and p covariates, S 3 has order max n 2 p t , np computational cost at iteration t where p t never exceeds the number of covariates switching spike-and-slab states between iterations t and t − 1 of the Markov chain. This improves upon the order n 2 p per-iteration cost of state-of-the-art implementations as, typically, p t is substantially smaller than p . We apply S 3 on synthetic and real-world datasets, demonstrating orders of magnitude speed-ups over existing exact samplers and significant gains in inferential quality over approximate samplers with comparable cost.