# Markov Chains on Orbits of Permutation Groups

arXiv: https://arxiv.org/abs/1408.2052 · HTML: https://mlsanity.com/paper/1408.2052/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2014.

## Built on by (most cited first, 2 of 2)

- [Towards Efficient MCMC Sampling in Bayesian Neural Networks by Exploiting Symmetry](https://mlsanity.com/paper/2304.02902/) (2023)
- [Colour Passing Revisited: Lifted Model Construction with Commutative Factors](https://mlsanity.com/paper/2309.11236/) (2023)

## Abstract (arXiv)

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.