2000 character limit reached
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.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.