Generalized Talagrand Inequality for Sinkhorn Distance using Entropy Power Inequality
Information Theory
2024-07-01 v1 math.IT
Machine Learning
Abstract
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.
Keywords
Cite
@article{arxiv.2109.08430,
title = {Generalized Talagrand Inequality for Sinkhorn Distance using Entropy Power Inequality},
author = {Shuchan Wang and Photios A. Stavrou and Mikael Skoglund},
journal= {arXiv preprint arXiv:2109.08430},
year = {2024}
}
Comments
The paper has been accepted to Information Theory Workshop 2021