Transport information Bregman divergences

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.

@article{li2025_2101.01162,
  title={ Transport information Bregman divergences },
  author={ Wuchen Li },
  journal={arXiv preprint arXiv:2101.01162},
  year={ 2025 }
}