Split-merge moves are a standard component of MCMC algorithms for tasks such as multi-target 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 better scaling to large data sets.
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