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Transport information Bregman divergences (2101.01162v2)
Published 4 Jan 2021 in cs.IT, cs.AI, math-ph, math.IT, math.MP, and math.PR
Abstract: We study Bregman divergences in probability density space embedded with the $L2$-Wasserstein metric. Several properties and dualities of transport Bregman divergences are provided. In particular, we derive the transport Kullback-Leibler (KL) divergence by a Bregman divergence of negative Boltzmann-Shannon entropy in $L2$-Wasserstein space. We also derive analytical formulas and generalizations of transport KL divergence for one-dimensional probability densities and Gaussian families.