# Transport information Bregman divergences

arXiv: https://arxiv.org/abs/2101.01162 · HTML: https://mlsanity.com/paper/2101.01162/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 4 Jan 2021.

## Builds on (most cited first, 5 of 5)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Natural gradient via optimal transport](https://mlsanity.com/paper/1803.07033/) (2018)
- [Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem](https://mlsanity.com/paper/1709.10219/) (2017)
- [Ambiguity set and learning via Bregman and Wasserstein](https://mlsanity.com/paper/1705.08056/) (2017)

## Built on by (most cited first, 3 of 3)

- [Information Geometry for Wasserstein KL Divergence of Gaussian Measures on ℝn](https://mlsanity.com/paper/2503.24022/) (2025)
- [Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Models](https://mlsanity.com/paper/2309.12997/) (2023)
- [Transport f divergences](https://mlsanity.com/paper/2504.15515/) (2025)

## Abstract (arXiv)

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.