Block-Value Symmetries in Probabilistic Graphical Models

TL;DR

This paper introduces block-value symmetries in probabilistic graphical models, generalizing existing symmetry concepts to improve lifted inference efficiency through new algorithms and heuristics.

Contribution

It defines BV symmetries, develops algorithms for their computation, and extends MCMC methods to leverage these symmetries for faster inference.

Findings

BV-MCMC mixes faster than traditional MCMC

BV symmetries capture more domain symmetries than VV symmetries

Proposed heuristics effectively identify beneficial block partitions

Abstract

One popular way for lifted inference in probabilistic graphical models is to first merge symmetric states into a single cluster (orbit) and then use these for downstream inference, via variations of orbital MCMC [Niepert, 2012]. These orbits are represented compactly using permutations over variables, and variable-value (VV) pairs, but they can miss several state symmetries in a domain. We define the notion of permutations over block-value (BV) pairs, where a block is a set of variables. BV strictly generalizes VV symmetries, and can compute many more symmetries for increasing block sizes. To operationalize use of BV permutations in lifted inference, we describe 1) an algorithm to compute BV permutations given a block partition of the variables, 2) BV-MCMC, an extension of orbital MCMC that can sample from BV orbits, and 3) a heuristic to suggest good block partitions. Our experiments show that BV-MCMC can mix much faster compared to vanilla MCMC and orbital MCMC.