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

TL;DR

This paper introduces a fast, stable, and parallelizable algorithm for elliptical slice sampling in linearly truncated multivariate normal distributions, significantly improving efficiency and numerical stability.

Contribution

The main contribution is an $ ext{O}(m ext{ log } m)$ algorithm for computing ellipse-polytope intersections, enhancing elliptical slice sampling methods.

Findings

Algorithm reduces computation time for intersection calculations.

Implementation improves numerical stability and parallelization.

Speeds up Markov chain Monte Carlo sampling in constrained spaces.

Abstract

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 $\mathcal{O}(m \log m)$ 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.