mlsanityData to 14 Oct 2026

Transport information Bregman divergences

arXiv 2101.01162 ↗First posted 4 Jan 2021cs.IT cs.AI math-phcited by 3

Not on the map. Why?

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.

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

5 of 40 references.

References · 5

  1. 2018Computational Optimal Transportcited by 780
  2. 2019On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract meanscited by 61
  3. 2018Natural gradient via optimal transportcited by 20
  4. 2017Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problemcited by 9
  5. 2017Ambiguity set and learning via Bregman and Wassersteincited by 4

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 0; 2025: 2.

3 papers.

  1. 2025Information Geometry for Wasserstein KL Divergence of Gaussian Measures on ℝncited by 1
  2. 2023Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Modelscited by 0
  3. 2025Transport f divergencescited by 0