Scalable Spike-and-Slab

Code

• github.com/niloyb/scalespikeslab
  OfficialIn papernone★ 6
• gitlab.com/AnonPaperCode/sss
  Officialnone★ 0

Abstract

Spike-and-slab priors are commonly used for Bayesian variable selection, due to their interpretability 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 and McCulloch (1993). For a dataset with n observations and p covariates, S^3 has order \ 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.

Tasks

Reproductions