# A Variational Inference method for Bayesian variable selection

arXiv: https://arxiv.org/abs/2211.11383 · HTML: https://mlsanity.com/paper/2211.11383/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Variational empirical Bayes variable selection in high-dimensional logistic regression](https://mlsanity.com/paper/2502.10532/) (2025)
- [Toward Embedding-Based Psychometrics: Structural Modeling of Assessment-Item Semantics With Contextual Scores](https://mlsanity.com/paper/2609.31976/) (2026)

## Abstract (arXiv)

Variable selection is a classic problem in statistics. In this paper, we consider a Bayes variable selection problem based on spike-and-slab prior with mixed normal distribution proposed by Rovckov'a and George (2014). Motivated by Ormerod and You (2017, 2023), we use the variational inference and collapsed variational inference method to solve the Bayesian problem instead of MCMC. Like Ormerod and You (2017, 2023), we also explain how the sparsity estimator is induced, and under certain mild assumptions, we also prove the consistent and asymptotic results.