Contextual Symmetries in Probabilistic Graphical Models
This work addresses the challenge of computational efficiency in probabilistic inference for researchers and practitioners in machine learning, representing an incremental improvement over previous symmetry-based methods.
The paper tackles the problem of efficient inference in probabilistic graphical models by introducing contextual symmetries, which extend existing symmetry definitions to allow states to be symmetric under specific variable assignments, and demonstrates that exploiting these symmetries leads to significant computational gains in experiments.
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.