Bayesian high-dimensional linear regression with generic spike-and-slab priors

2019/12/19 by Bai Jiang, Qiang Sun, Jiang, Bai +1
Computer Science · Engineering · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1912.08993

openalex publication_date 2019/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and analyses, and thus can not be generalized directly. In this paper, we propose a class of generic spike-and-slab priors and develop a unified framework to rigorously assess their theoretical properties. Technically, we provide general conditions under which generic spike-and-slab priors can achieve the nearly-optimal posterior contraction rate and the model selection consistency. Our results include those of Narisetty and He (2014) and Castillo et al. (2015) as special cases.

Citations

• Nearly unbiased variable selection under minimax concave penalty
• The horseshoe estimator for sparse signals
• Nearly optimal Bayesian Shrinkage for High Dimensional Regression

Related

• A Variational Spike-and-Slab Approach for Group Variable Selection
• Nearly optimal Bayesian Shrinkage for High Dimensional Regression
• Scalable Spike-and-Slab
• From Estimation to Sampling for Bayesian Linear Regression with Spike-and-Slab Prior
• Bayesian Regression Using a Prior on the Model Fit: The R2-D2 Shrinkage Prior