Complexity Bounds for Dirichlet Process Slice Samplers

Beatrice Franzolini, Francesco Gaffi
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:31553-31574, 2026.

Abstract

Slice sampling is a standard Monte Carlo technique for Dirichlet process (DP)-based models, widely used in posterior simulation. However, formal assessments of the scalability of posterior slice samplers have remained largely unexplored, primarily because the computational cost of a slice-sampling iteration is random and potentially unbounded. In this work, we obtain high-probability bounds on the computational complexity of DP slice samplers. Our main results show that, uniformly across posterior cluster-growth regimes, the overhead induced by slice variables, relatively to the number of clusters supported by the posterior, is $O_{\mathbb P}(\log n)$. As a consequence, even in worst-case configurations, superlinear blow-ups in per-iteration computational cost occur with vanishing probability. Our analysis applies broadly to DP–based models without any likelihood-specific assumptions, still providing complexity guarantees for posterior sampling on arbitrary datasets. These results establish a theoretical foundation for assessing the practical scalability of slice sampling in DP-based models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-franzolini26a, title = {Complexity Bounds for {D}irichlet Process Slice Samplers}, author = {Franzolini, Beatrice and Gaffi, Francesco}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {31553--31574}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/franzolini26a/franzolini26a.pdf}, url = {https://proceedings.mlr.press/v306/franzolini26a.html}, abstract = {Slice sampling is a standard Monte Carlo technique for Dirichlet process (DP)-based models, widely used in posterior simulation. However, formal assessments of the scalability of posterior slice samplers have remained largely unexplored, primarily because the computational cost of a slice-sampling iteration is random and potentially unbounded. In this work, we obtain high-probability bounds on the computational complexity of DP slice samplers. Our main results show that, uniformly across posterior cluster-growth regimes, the overhead induced by slice variables, relatively to the number of clusters supported by the posterior, is $O_{\mathbb P}(\log n)$. As a consequence, even in worst-case configurations, superlinear blow-ups in per-iteration computational cost occur with vanishing probability. Our analysis applies broadly to DP–based models without any likelihood-specific assumptions, still providing complexity guarantees for posterior sampling on arbitrary datasets. These results establish a theoretical foundation for assessing the practical scalability of slice sampling in DP-based models.} }
Endnote
%0 Conference Paper %T Complexity Bounds for Dirichlet Process Slice Samplers %A Beatrice Franzolini %A Francesco Gaffi %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-franzolini26a %I PMLR %P 31553--31574 %U https://proceedings.mlr.press/v306/franzolini26a.html %V 306 %X Slice sampling is a standard Monte Carlo technique for Dirichlet process (DP)-based models, widely used in posterior simulation. However, formal assessments of the scalability of posterior slice samplers have remained largely unexplored, primarily because the computational cost of a slice-sampling iteration is random and potentially unbounded. In this work, we obtain high-probability bounds on the computational complexity of DP slice samplers. Our main results show that, uniformly across posterior cluster-growth regimes, the overhead induced by slice variables, relatively to the number of clusters supported by the posterior, is $O_{\mathbb P}(\log n)$. As a consequence, even in worst-case configurations, superlinear blow-ups in per-iteration computational cost occur with vanishing probability. Our analysis applies broadly to DP–based models without any likelihood-specific assumptions, still providing complexity guarantees for posterior sampling on arbitrary datasets. These results establish a theoretical foundation for assessing the practical scalability of slice sampling in DP-based models.
APA
Franzolini, B. & Gaffi, F.. (2026). Complexity Bounds for Dirichlet Process Slice Samplers. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:31553-31574 Available from https://proceedings.mlr.press/v306/franzolini26a.html.

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