# A Fast, Robust Elliptical Slice Sampling Implementation for Linearly Truncated Multivariate Normal Distributions

arXiv: https://arxiv.org/abs/2407.10449 · HTML: https://mlsanity.com/paper/2407.10449/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 4 of 4)

- [Towards Practical Preferential Bayesian Optimization with Skew Gaussian Processes](https://mlsanity.com/paper/2302.01513/) (2023)
- [Evaluating State-of-the-Art Classification Models Against Bayes Optimality](https://mlsanity.com/paper/2106.03357/) (2021)
- [Integrals over Gaussians under Linear Domain Constraints](https://mlsanity.com/paper/1910.09328/) (2019)
- [A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes](https://mlsanity.com/paper/2012.06846/) (2020)

## Built on by (most cited first, 1 of 1)

- [Knowledge Gradient for Preference Learning](https://mlsanity.com/paper/2601.22335/) (2026)

## Abstract (arXiv)

Elliptical slice sampling, when adapted to linearly truncated multivariate normal distributions, is a rejection-free Markov chain Monte Carlo method. At its core, it requires analytically constructing an ellipse-polytope intersection. The main novelty of this paper is an algorithm that computes this intersection in O(m log m) time, where m is the number of linear inequality constraints representing the polytope. We show that an implementation based on this algorithm enhances numerical stability, speeds up running time, and is easy to parallelize for launching multiple Markov chains.