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Divergence is not only an important mathematical concept in informationtheory, but also applied to machine learning problems such as low-dimensionalembedding, manifold learning, clustering, classification, and anomalydetection. We proposed a bayesian model---co-BPM---to characterize thediscrepancy of two sample sets, i.e., to estimate the divergence of theirunderlying distributions. In order to avoid the pitfalls of plug-in methodsthat estimate each density independently, our bayesian model attempts to learna coupled binary partition of the sample space that best captures thelandscapes of both distributions, then make direct inference on theirdivergences. The prior is constructed by leveraging the sequential buildup ofthe coupled binary partitions and the posterior is sampled via our specializedMCMC. Our model provides a unified way to estimate various types of divergencesand enjoys convincing accuracy. We demonstrate its effectiveness throughsimulations, comparisons with the \emph{state-of-the-art} and a real dataexample.

co-BPM: a Bayesian Model for Divergence Estimation