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On the sample complexity of entropic optimal transport

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arxiv 2206.13472 v1 pith:OYX4MHOC submitted 2022-06-27 math.ST stat.TH

Philippe Rigollet , Austin J. Stromme This is my paper · ORCID
classification math.STstat.TH
keywords entropicoptimaltransportcomplexityparametricratesregressionsample
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We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for estimating various quantities of interest, including the entropic regression function which is a natural analog to the optimal transport map. As an application, we propose a practical model for transfer learning based on entropic optimal transport and establish parametric rates of convergence for nonparametric regression and classification.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Computational and Statistical Guarantees of the \textit{c}-Rectified flow

    stat.ML 2026-08 conditional novelty 6.0 of 10

    Iterative c-rectified flow converges to optimal transport under regularity assumptions, and score-based plug-in estimation yields near-optimal transport-map rates.

  2. Optimal Transport under Group Fairness Constraints

    stat.ML 2026-01 conditional novelty 6.0 of 10

    Group-fairness targets are added as constraints to entropic optimal transport, with a modified Sinkhorn algorithm and two relaxations (penalty and cost learning) that come with sample-complexity bounds.

  3. Distributional Limit Theory for Optimal Transport

    math.ST 2025-05 conditional novelty 5.0 of 10

    A survey of central limit theorems for empirical optimal transport, with a new one-dimensional L1 cost fluctuation CLT and a list of open problems.

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