Merge-split Markov chain Monte Carlo for community detection
This addresses the challenge of accurate community detection in networks for researchers and practitioners, though it is incremental as it builds on existing MCMC and SBM frameworks.
The authors tackled the problem of efficiently sampling network partitions from the posterior distribution under the stochastic block model, and their merge-split MCMC scheme improved mixing times by several orders of magnitude compared to single-node move methods.
We present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We demonstrate how schemes based on the move of single nodes between groups systematically fail at correctly sampling from the posterior distribution even on small networks, and how our merge-split approach behaves significantly better, and improves the mixing time of the Markov chain by several orders of magnitude in typical cases. We also show how the scheme can be straightforwardly extended to nested versions of the SBM, yielding asymptotically exact samples of hierarchical network partitions.