Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature
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.
Cite
Text
Williams et al. "Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature." Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, 2025.Markdown
[Williams et al. "Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature." Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, 2025.](https://mlanthology.org/uai/2025/williams2025uai-geodesic/)BibTeX
@inproceedings{williams2025uai-geodesic,
title = {{Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature}},
author = {Williams, Bernardo and Yu, Hanlin and Luu, Hoang Phuc Hau and Arvanitidis, Georgios and Klami, Arto},
booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence},
year = {2025},
pages = {4543-4564},
volume = {286},
url = {https://mlanthology.org/uai/2025/williams2025uai-geodesic/}
}