Non-Count Symmetries in Boolean & Multi-Valued Prob. Graphical Models

TL;DR

This paper introduces algorithms to identify non-count symmetries in Boolean and multi-valued probabilistic graphical models, enabling more efficient lifted inference by capturing a broader class of symmetries.

Contribution

The authors develop the first algorithms to compute non-count symmetries, including symmetries between multi-valued variables with different domain sizes.

Findings

Exploiting non-count symmetries improves inference efficiency.

Algorithms find symmetries missed by previous methods.

Experiments show significant computational gains in MCMC.

Abstract

Lifted inference algorithms commonly exploit symmetries in a probabilistic graphical model (PGM) for efficient inference. However, existing algorithms for Boolean-valued domains can identify only those pairs of states as symmetric, in which the number of ones and zeros match exactly (count symmetries). Moreover, algorithms for lifted inference in multi-valued domains also compute a multi-valued extension of count symmetries only. These algorithms miss many symmetries in a domain. In this paper, we present first algorithms to compute non-count symmetries in both Boolean-valued and multi-valued domains. Our methods can also find symmetries between multi-valued variables that have different domain cardinalities. The key insight in the algorithms is that they change the unit of symmetry computation from a variable to a variable-value (VV) pair. Our experiments find that exploiting these symmetries in MCMC can obtain substantial computational gains over existing algorithms.