# A Variational Algorithm for Bayesian Variable Selection

arXiv: https://arxiv.org/abs/1602.07640 · HTML: https://mlsanity.com/paper/1602.07640/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2016.

## Built on by (most cited first, 6 of 6)

- [Spike and slab Bayesian sparse principal component analysis](https://mlsanity.com/paper/2102.00305/) (2021)
- [Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm](https://mlsanity.com/paper/2209.08139/) (2022)
- [Stability of Sequential and Parallel Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2603.20929/) (2026)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [Variational empirical Bayes variable selection in high-dimensional logistic regression](https://mlsanity.com/paper/2502.10532/) (2025)
- [Robust Variational Bayes by Min-Max Median Aggregation](https://mlsanity.com/paper/2512.12676/) (2025)

## Abstract (arXiv)

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is incorporated by the so-called spike-and-slab prior on the coefficients. Instead of replying on MCMC for posterior inference, we propose a fast and scalable algorithm based on variational approximation to the posterior distribution. The updating scheme employed by our algorithm is different from the one proposed by Carbonetto and Stephens (2012). Those changes seem crucial for us to show that our algorithm can achieve asymptotic consistency even when the feature dimension diverges exponentially fast with the sample size. Empirical results have demonstrated the effectiveness and efficiency of the proposed algorithm.