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Computer Science > Information Theory

arXiv:2109.08430 (cs)
[Submitted on 17 Sep 2021]

Title:Generalized Talagrand Inequality for Sinkhorn Distance using Entropy Power Inequality

Authors:Shuchan Wang, Photios A. Stavrou, Mikael Skoglund
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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.
Comments: The paper has been accepted to Information Theory Workshop 2021
Subjects: Information Theory (cs.IT); Machine Learning (stat.ML)
Cite as: arXiv:2109.08430 [cs.IT]
  (or arXiv:2109.08430v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2109.08430
Related DOI: https://doi.org/10.1109/ITW48936.2021.9611464

Submission history

From: Shuchan Wang [view email]
[v1] Fri, 17 Sep 2021 09:44:27 UTC (2,436 KB)
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