  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.
