Markov Chains on Orbits of Permutation Groups
  We present a novel approach to detecting and utilizing symmetries in
probabilistic graphical models with two main contributions. First, we present a
scalable approach to computing generating sets of permutation groups
representing the symmetries of graphical models. Second, we introduce orbital
Markov chains, a novel family of Markov chains leveraging model symmetries to
reduce mixing times. We establish an insightful connection between model
symmetries and rapid mixing of orbital Markov chains. Thus, we present the
first lifted MCMC algorithm for probabilistic graphical models. Both analytical
and empirical results demonstrate the effectiveness and efficiency of the
approach.
