Bayesian Bootstrap Spike-and-Slab LASSO

The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find local posterior modes. Trading off uncertainty quantification...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 118; no. 543; pp. 2013 - 2028
Main Authors: Nie, Lizhen, Ročková, Veronika
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.07.2023
Taylor & Francis Ltd
Subjects:
Algorithms
Bayesian analysis
Bayesian bootstrap
Bayesian theory
Bootstrap method
data collection
Measurement
Optimization
Posterior contraction
Sampling
Shrinkage
Spike-and-Slab LASSO
Statistics
Truth
Uncertainty
Weighted likelihood bootstrap
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary:The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find local posterior modes. Trading off uncertainty quantification for computational speed, these strategies have enabled spike-and-slab deployments at scales that would be previously unfeasible. We build on one recent development in this strand of work: the Spike-and-Slab LASSO procedure. Instead of optimization, however, we explore multiple avenues for posterior sampling, some traditional and some new. Intrigued by the speed of Spike-and-Slab LASSO mode detection, we explore the possibility of sampling from an approximate posterior by performing MAP optimization on many independently perturbed datasets. To this end, we explore Bayesian bootstrap ideas and introduce a new class of jittered Spike-and-Slab LASSO priors with random shrinkage targets. These priors are a key constituent of the Bayesian Bootstrap Spike-and-Slab LASSO (BB-SSL) method proposed here. BB-SSL turns fast optimization into approximate posterior sampling. Beyond its scalability, we show that BB-SSL has a strong theoretical support. Indeed, we find that the induced pseudo-posteriors contract around the truth at a near-optimal rate in sparse normal-means and in high-dimensional regression. We compare our algorithm to the traditional Stochastic Search Variable Selection (under Laplace priors) as well as many state-of-the-art methods for shrinkage priors. We show, both in simulations and on real data, that our method fares very well in these comparisons, often providing substantial computational gains. Supplementary materials for this article are available online.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2022.2025815