A Smart-Dumb/Dumb-Smart Algorithm for Efficient Split-Merge MCMC

Abstract

Split-merge moves are a standard component of MCMC algorithms for tasks such as multitarget tracking and fitting mixture models with unknown numbers of components. Achieving rapid mixing for split-merge MCMC has been notoriously difficult, and state-of-the-art methods do not scale well. We explore the reasons for this and propose a new split-merge kernel consisting of two sub-kernels: one combines a ``smart'' split move that proposes plausible splits of heterogeneous clusters with a ``dumb'' merge move that proposes merging random pairs of clusters; the other combines a dumb split move with a smart merge move. We show that the resulting smart-dumb/dumb-smart (SDDS) algorithm outperforms previous methods. Experiments with entity-mention models and Dirichlet process mixture models demonstrate much faster convergence and much better scaling to large data sets.