# Bayesian Variable Selection in a Million Dimensions

arXiv: https://arxiv.org/abs/2208.01180 · HTML: https://mlsanity.com/paper/2208.01180/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 2 Aug 2022.

## Builds on (most cited first, 3 of 3)

- [The Hamming Ball Sampler](https://mlsanity.com/paper/1504.08133/) (2015)
- [Scalable Importance Tempering and Bayesian Variable Selection](https://mlsanity.com/paper/1805.00541/) (2018)
- [Scalable Spike-and-Slab](https://mlsanity.com/paper/2204.01668/) (2022)

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

- [Position: Biology is the Challenge Physics-Informed ML Needs to Evolve](https://mlsanity.com/paper/2510.25368/) (2025)
- [Variable-Complexity Weighted-Tempered Gibbs Samplers for Bayesian Variable Selection](https://mlsanity.com/paper/2304.02899/) (2023)

## Abstract (arXiv)

Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been hampered by computational challenges, especially in difficult regimes with a large number of covariates P or non-conjugate likelihoods. To scale to the large P regime we introduce an efficient MCMC scheme whose cost per iteration is sublinear in P. In addition we show how this scheme can be extended to generalized linear models for count data, which are prevalent in biology, ecology, economics, and beyond. In particular we design efficient algorithms for variable selection in binomial and negative binomial regression, which includes logistic regression as a special case. In experiments we demonstrate the effectiveness of our methods, including on cancer and maize genomic data.