Transport information Bregman divergences

Wuchen Li

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arXiv · 2101.01162

Transport information Bregman divergences

Wuchen Li

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Abstract

We study Bregman divergences in probability density space embedded with the $L^2$-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 $L^2$-Wasserstein space. We also derive analytical formulas and generalizations of transport KL divergence for one-dimensional probability densities and Gaussian families.

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BibTeX RIS

Wuchen Li. 2021-01-04. Transport information Bregman divergences. https://arxiv.org/abs/2101.01162

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