Gibbsian Polar Slice Sampling

Philip Schär, Michael Habeck, Daniel Rudolf
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:30204-30223, 2023.

Abstract

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-schar23a, title = {Gibbsian Polar Slice Sampling}, author = {Sch\"{a}r, Philip and Habeck, Michael and Rudolf, Daniel}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {30204--30223}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/schar23a/schar23a.pdf}, url = {https://proceedings.mlr.press/v202/schar23a.html}, abstract = {Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.} }
Endnote
%0 Conference Paper %T Gibbsian Polar Slice Sampling %A Philip Schär %A Michael Habeck %A Daniel Rudolf %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-schar23a %I PMLR %P 30204--30223 %U https://proceedings.mlr.press/v202/schar23a.html %V 202 %X Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.
APA
Schär, P., Habeck, M. & Rudolf, D.. (2023). Gibbsian Polar Slice Sampling. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:30204-30223 Available from https://proceedings.mlr.press/v202/schar23a.html.

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