# Bayesian Bootstrap Spike-and-Slab LASSO

arXiv: https://arxiv.org/abs/2011.14279 · HTML: https://mlsanity.com/paper/2011.14279/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2020.

## Built on by (most cited first, 8 of 8)

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- [GEMSS: A Variational Method for Discovering Multiple Sparse Solutions in Classification and Regression Problems](https://mlsanity.com/paper/2602.08913/) (2026)
- [Nonparametric posterior learning for emission tomography with multimodal data](https://mlsanity.com/paper/2108.00866/) (2021)
- [Centroid Approximation for Bootstrap: Improving Particle Quality at Inference](https://mlsanity.com/paper/2110.08720/) (2021)
- [Bayesian Analysis for Over-parameterized Linear Model via Effective Spectra](https://mlsanity.com/paper/2305.15754/) (2023)
- [Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation Discovery](https://mlsanity.com/paper/2306.17038/) (2023)

## Abstract (arXiv)

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 of Rovckov'a and George (2018). 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 superbly in these comparisons, often providing substantial computational gains.