Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature

TL;DR

This paper introduces a novel slice sampling method that approximates geodesics via differential equations, improving exploration in multimodal distributions with strong curvature where traditional methods struggle.

Contribution

It generalizes Hit-and-Run slice sampling to complex geometries by approximating geodesics, enabling better sampling in challenging multimodal and highly curved distributions.

Findings

Enhanced exploration of multimodal distributions.

Improved sampling efficiency in high-curvature regions.

Demonstrated advantages over existing methods on challenging problems.

Abstract

Traditional Markov Chain Monte Carlo sampling methods often struggle with sharp curvatures, intricate geometries, and multimodal distributions. Slice sampling can resolve local exploration inefficiency issues, and Riemannian geometries help with sharp curvatures. Recent extensions enable slice sampling on Riemannian manifolds, but they are restricted to cases where geodesics are available in a closed form. We propose a method that generalizes Hit-and-Run slice sampling to more general geometries tailored to the target distribution, by approximating geodesics as solutions to differential equations. Our approach enables the exploration of the regions with strong curvature and rapid transitions between modes in multimodal distributions. We demonstrate the advantages of the approach over challenging sampling problems.