Markov Chains on Orbits of Permutation Groups

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.

To appear in Proceedings of UAI2012

References in corpus (6)

• Improving the Accuracy and Efficiency of MAP Inference for Markov Logic
• Counting Belief Propagation
• Probabilistic Theorem Proving
• General-Purpose MCMC Inference over Relational Structures
• Bisimulation-based Approximate Lifted Inference
• Improved Mixing Condition on the Grid for Counting and Sampling Independent Sets

Cited by in corpus (9)

• Equivariance Through Parameter-Sharing
• Quantum Enhanced Inference in Markov Logic Networks
• Automorphism Groups of Graphical Models and Lifted Variational Inference
• Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
• Contextual Symmetries in Probabilistic Graphical Models
• Symmetry-Aware Marginal Density Estimation
• Block-Value Symmetries in Probabilistic Graphical Models
• Lifted Marginal MAP Inference
• Lifted Message Passing for the Generalized Belief Propagation