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This is the project page for Orbital Markov Chains and the symmetry-aware Rao-Blackwell estimator both of which make probabilistic inference more efficient under model symmetries. The theory and some applications are described in the papers Markov Chains on Orbits of Permutation Groups and Symmetry-Aware Marginal Density Estimation.
Orbital Markov Chains are the first generally applicable class of symmetry-aware (lifted in SRL terms) MCMC algorithms for probabilistic inference. Orbital Markov chains implicitly operate on a partition of the original state space. Orbital Markov chains mix more rapidly whenever there is symmetry in the model under consideration. Despite their exotic name, orbital Markov chains work with very large graphical models!
The symmetry-aware Rao-Blackwell estimator
