Spike and Slab Variable Selection via EMVS

• Activity Number: 434
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Veronika Rockova*+ and Edward George
• Companies: Wharton School and Wharton School
• Keywords: EMVS ; Bayesian variable selection ; High-dimensional ; Spike and slab

Abstract

EMVS is a fast deterministic approach to identifying sparse high posterior models for Bayesian variable selection under spike-and-slab priors. We consider the variable selection properties of the EMVS procedure under the unifying framework of regularized least squares with non-concave penalties. Optimal EMVS calibrations are derived that guarantee the recoverability of the true sparse model with probability tending to one. Heavy-tailed spike and slab formulations will be described that ameliorate the bias problems associated with Gaussian spike and slab priors. Motivated by the asymptotic arguments, we investigate the usefulness of determinantal variable selection priors, which provide prior support on recoverable subsets, penalize redundancy in model selection and thereby alleviate the multi-modality associated with collinear predictors. The presented methodology will be illustrated on a practical example of finding extreme non-additive effects in a high-dimensional ANOVA model.