Uncertainty in Artificial Intelligence
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Markov Chains on Orbits of Permutation Groups
Mathias Niepert
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.
Keywords:
Pages: 624-633
PS Link:
PDF Link: /papers/12/p624-niepert.pdf
BibTex:
@INPROCEEDINGS{Niepert12,
AUTHOR = "Mathias Niepert ",
TITLE = "Markov Chains on Orbits of Permutation Groups",
BOOKTITLE = "Proceedings of the Twenty-Eighth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-12)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2012",
PAGES = "624--633"
}


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