Contextual Symmetries in Probabilistic Graphical Models

TL;DR

This paper introduces the concept of contextual symmetry in probabilistic graphical models, allowing for more flexible symmetry exploitation during inference, leading to significant computational improvements.

Contribution

It extends existing symmetry definitions by introducing contextual symmetry, which captures more complex symmetries via graph isomorphism, enhancing inference efficiency.

Findings

Contextual symmetry generalizes previous symmetry notions.

Exploiting contextual symmetry improves inference efficiency.

Experimental results show significant computational gains.

Abstract

An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run over the lifted graphical model instead of the flat one. Our paper extends existing definitions of symmetry by introducing the novel notion of contextual symmetry. Two states that are not globally symmetric, can be contextually symmetric under some specific assignment to a subset of variables, referred to as the context variables. Contextual symmetry subsumes previous symmetry definitions and can rep resent a large class of symmetries not representable earlier. We show how to compute contextual symmetries by reducing it to the problem of graph isomorphism. We extend previous work on exploiting symmetries in the MCMC framework to the case of contextual symmetries. Our experiments on several domains of interest demonstrate that exploiting contextual symmetries can result in significant computational gains.