Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature

Bernardo Williams, Hanlin Yu, Hoang Phuc Hau Luu, Georgios Arvanitidis, Arto Klami
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:4543-4564, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v286-williams25a, 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}, pages = {4543--4564}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/williams25a/williams25a.pdf}, url = {https://proceedings.mlr.press/v286/williams25a.html}, 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.} }
Endnote
%0 Conference Paper %T Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature %A Bernardo Williams %A Hanlin Yu %A Hoang Phuc Hau Luu %A Georgios Arvanitidis %A Arto Klami %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-williams25a %I PMLR %P 4543--4564 %U https://proceedings.mlr.press/v286/williams25a.html %V 286 %X 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.
APA
Williams, B., Yu, H., Luu, H.P.H., Arvanitidis, G. & Klami, A.. (2025). Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:4543-4564 Available from https://proceedings.mlr.press/v286/williams25a.html.

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