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

2023/07/09 by Qijia Jiang, Jiang, Qijia
Computer Science · Engineering · #Blind Source Separation Techniques #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2307.05558

openalex publication_date 2023/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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