# Generalized Talagrand Inequality for Sinkhorn Distance using Entropy Power Inequality

arXiv: https://arxiv.org/abs/2109.08430 · HTML: https://mlsanity.com/paper/2109.08430/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 17 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Policy Optimization as Wasserstein Gradient Flows](https://mlsanity.com/paper/1808.03030/) (2018)
- [Uncoupled isotonic regression via minimum Wasserstein deconvolution](https://mlsanity.com/paper/1806.10648/) (2018)
- [Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover](https://mlsanity.com/paper/2008.10249/) (2020)

## Built on by (most cited first, 1 of 1)

- [Information-Theoretic Equivalence of Entropic Multi-Marginal Optimal Transport: A Theory for Multi-Agent Communication](https://mlsanity.com/paper/2208.10256/) (2022)

## Abstract (arXiv)

In this paper, we study the connection between entropic optimal transport and entropy power inequality (EPI). First, we prove an HWI-type inequality making use of the infinitesimal displacement convexity of optimal transport map. Second, we derive two Talagrand-type inequalities using the saturation of EPI that corresponds to a numerical term in our expression. We evaluate for a wide variety of distributions this term whereas for Gaussian and i.i.d. Cauchy distributions this term is found in explicit form. We show that our results extend previous results of Gaussian Talagrand inequality for Sinkhorn distance to the strongly log-concave case.