# Scalable Importance Tempering and Bayesian Variable Selection

arXiv: https://arxiv.org/abs/1805.00541 · HTML: https://mlsanity.com/paper/1805.00541/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2018.

## Built on by (most cited first, 9 of 9)

- [Dimension-free Relaxation Times of Informed MCMC Samplers on Discrete Spaces](https://mlsanity.com/paper/2404.03867/) (2024)
- [Fast Bayesian Variable Selection in Binomial and Negative Binomial Regression](https://mlsanity.com/paper/2106.14981/) (2021)
- [Bayesian Variable Selection in a Million Dimensions](https://mlsanity.com/paper/2208.01180/) (2022)
- [Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering](https://mlsanity.com/paper/2211.16041/) (2022)
- [Importance is Important: Generalized Markov Chain Importance Sampling Methods](https://mlsanity.com/paper/2304.06251/) (2023)
- [Robust leave-one-out cross-validation for high-dimensional Bayesian models](https://mlsanity.com/paper/2209.09190/) (2022)
- [Variable-Complexity Weighted-Tempered Gibbs Samplers for Bayesian Variable Selection](https://mlsanity.com/paper/2304.02899/) (2023)
- [From Minimax Optimal Importance Sampling to Uniformly Ergodic Importance-tempered MCMC](https://mlsanity.com/paper/2506.19186/) (2025)
- [UbiQVision: Quantifying Uncertainty in XAI for Image Recognition](https://mlsanity.com/paper/2512.20288/) (2025)

## Abstract (arXiv)

We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard schemes. When applied to Bayesian variable-selection problems, the novel algorithm is orders of magnitude more efficient than available alternative sampling schemes and enables fast and reliable fully Bayesian inferences with tens of thousand regressors.