Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature

Bernardo Williams, Hanlin Yu, Hoang Phuc Hau Luu, Georgios Arvanitidis, Arto Klami

Keywords: Markov Chain Monte Carlo (MCMC), Slice Sampling, Riemannian Geometry, Hit-and-Run Sampling

TL;DR: We generalize slice sampling by approximating geodesics, enabling efficient sampling in complex geometries and multimodal distributions.

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.

Code Link: https://github.com/williwilliams3/magss

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission293/Authors, auai.org/UAI/2025/Conference/Submission293/Reproducibility_Reviewers

Submission Number: 293