# From Estimation to Sampling for Bayesian Linear Regression with Spike-and-Slab Prior

arXiv: https://arxiv.org/abs/2307.05558 · HTML: https://mlsanity.com/paper/2307.05558/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 9 Jul 2023.

## Builds on (most cited first, 7 of 7)

- [Improved analysis for a proximal algorithm for sampling](https://mlsanity.com/paper/2202.06386/) (2022)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization](https://mlsanity.com/paper/2203.05093/) (2022)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [Bayesian linear regression with sparse priors](https://mlsanity.com/paper/1403.0735/) (2014)
- [On the Computational Complexity of High-Dimensional Bayesian Variable Selection](https://mlsanity.com/paper/1505.07925/) (2015)
- [Scalable Spike-and-Slab](https://mlsanity.com/paper/2204.01668/) (2022)

## Abstract (arXiv)

We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically and computationally) is investigated and two algorithms based on Gibbs sampling and Stochastic Localization are analyzed, both under the same (quite natural) statistical assumptions that also enable valid inference on the sparse planted signal. The benefit of the Stochastic Localization sampler is particularly prominent for data matrix that is not well-designed.