Variational Bayes for High-Dimensional Linear Regression With Sparse Priors

• 成果类型: Article
• 署名作者: Ray, Kolyan; Szabo, Botond
• 署名单位: Imperial College London; Vrije Universiteit Amsterdam
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1847121
• 发表日期: 2022
• 页码: 1270-1281
• 关键词: Empirical Bayes; variable selection; posterior concentration; convergence-rates; inference; needles; straw; spike

摘要

We study a mean-field spike and slab variational Bayes (VB) approximation to Bayesian model selection priors in sparse high-dimensional linear regression. Under compatibility conditions on the design matrix, oracle inequalities are derived for the mean-field VB approximation, implying that it converges to the sparse truth at the optimal rate and gives optimal prediction of the response vector. The empirical performance of our algorithm is studied, showing that it works comparably well as other state-of-the-art Bayesian variable selection methods. We also numerically demonstrate that the widely used coordinate-ascent variational inference algorithm can be highly sensitive to the parameter updating order, leading to potentially poor performance. To mitigate this, we propose a novel prioritized updating scheme that uses a data-driven updating order and performs better in simulations. The variational algorithm is implemented in the R package sparsevb. for this article are available online.