# Spike and slab variational Bayes for high dimensional logistic regression

arXiv: https://arxiv.org/abs/2010.11665 · HTML: https://mlsanity.com/paper/2010.11665/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 16 of 16)

- [VICE: Variational Interpretable Concept Embeddings](https://mlsanity.com/paper/2205.00756/) (2022)
- [Variational Inference in high-dimensional linear regression](https://mlsanity.com/paper/2104.12232/) (2021)
- [On the inability of Gaussian process regression to optimally learn compositional functions](https://mlsanity.com/paper/2205.07764/) (2022)
- [Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selection](https://mlsanity.com/paper/2207.11208/) (2022)
- [Scalable Spike-and-Slab](https://mlsanity.com/paper/2204.01668/) (2022)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression](https://mlsanity.com/paper/2309.16843/) (2023)
- [Variational Bayes for high-dimensional proportional hazards models with applications within gene expression](https://mlsanity.com/paper/2112.10270/) (2021)
- [Covariate-Elaborated Robust Partial Information Transfer with Conditional Spike-and-Slab Prior](https://mlsanity.com/paper/2404.03764/) (2024)
- [Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion prior](https://mlsanity.com/paper/2310.00097/) (2023)
- [Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variance](https://mlsanity.com/paper/2405.19016/) (2024)
- [Logistic Variational Bayes Revisited](https://mlsanity.com/paper/2406.00713/) (2024)
- [Variational empirical Bayes variable selection in high-dimensional logistic regression](https://mlsanity.com/paper/2502.10532/) (2025)
- [Variational Task Vector Composition](https://mlsanity.com/paper/2509.18208/) (2025)
- [BaGGLS: A Bayesian Shrinkage Framework for Interpretable Modeling of Interactions in High-Dimensional Biological Data](https://mlsanity.com/paper/2511.15330/) (2025)
- [A Flexible Empirical Bayes Approach to Generalized Linear Models, with Applications to Sparse Logistic Regression](https://mlsanity.com/paper/2601.21217/) (2026)

## Abstract (arXiv)

Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional logistic regression. We provide non-asymptotic theoretical guarantees for the VB posterior in both ℓ2 and prediction loss for a sparse truth, giving optimal (minimax) convergence rates. Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices. We confirm the improved performance of our VB algorithm over common sparse VB approaches in a numerical study.