co-BPM: a Bayesian Model for Estimating Divergence and Distance of Distributions

A Bayesian model is proposed to characterize the discrepancy of two samples, e.g., to estimate the divergence or distance of their underlying distributions. The core idea of this framework is to learn a partition of the sample space that best captures the landscapes of their distributions. In order to avoid the pitfalls of plug-in methods that estimate each sample density independently with respect to the Lebesgue measure, we make direct inference on the two distributions simultaneously from a joint prior, i.e., the coupled binary partition prior. Our prior leverages on the class of piecewise constant functions built upon binary partitions of the domain. Our model ushers a unified way to estimate various types of discrepancies between samples and enjoys convincing accuracy. We demonstrate its effectiveness through simulations and comparisons.