Bayesian l0‐regularized least squares

Nicholas G. Polson and Lei Sun

Applied Stochastic Models in Business and Industry, 2019, vol. 35, issue 3, 717-731

Abstract: Bayesian l0‐regularized least squares is a variable selection technique for high‐dimensional predictors. The challenge is optimizing a nonconvex objective function via search over model space consisting of all possible predictor combinations. Spike‐and‐slab (aka Bernoulli‐Gaussian) priors are the gold standard for Bayesian variable selection, with a caveat of computational speed and scalability. Single best replacement (SBR) provides a fast scalable alternative. We provide a link between Bayesian regularization and proximal updating, which provides an equivalence between finding a posterior mode and a posterior mean with a different regularization prior. This allows us to use SBR to find the spike‐and‐slab estimator. To illustrate our methodology, we provide simulation evidence and a real data example on the statistical properties and computational efficiency of SBR versus direct posterior sampling using spike‐and‐slab priors. Finally, we conclude with directions for future research.

Date: 2019
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https://doi.org/10.1002/asmb.2381

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:35:y:2019:i:3:p:717-731

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