Emergent Mind
Transport information Bregman divergences
(2101.01162)
Published Jan 4, 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.
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