Markov Chains on Orbits of Permutation Groups

Mathias Niepert
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:622-632, 2012.

Abstract

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models. Both analytical and empirical results demonstrate the effectiveness and efficiency of the approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-niepert12a, title = {{M}arkov Chains on Orbits of Permutation Groups}, author = {Niepert, Mathias}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {622--632}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/niepert12a/niepert12a.pdf}, url = {https://proceedings.mlr.press/r10/niepert12a.html}, abstract = {We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models. Both analytical and empirical results demonstrate the effectiveness and efficiency of the approach.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Markov Chains on Orbits of Permutation Groups %A Mathias Niepert %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-niepert12a %I PMLR %P 622--632 %U https://proceedings.mlr.press/r10/niepert12a.html %V R10 %X We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models. Both analytical and empirical results demonstrate the effectiveness and efficiency of the approach. %Z Reissued by PMLR on 04 October 2026.
APA
Niepert, M.. (2012). Markov Chains on Orbits of Permutation Groups. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:622-632 Available from https://proceedings.mlr.press/r10/niepert12a.html. Reissued by PMLR on 04 October 2026.

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