mlsanityData to 7 Oct 2026

An improved central limit theorem and fast convergence rates for entropic transportation costs

arXiv 2204.09105 ↗First posted 19 Apr 2022math.ST cs.LG math.PRcited by 18

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Abstract (arXiv)

We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal transport between measures which are not necessarily discrete. In the compactly supported case, we complement these results with new, faster, convergence rates for the expected entropic transportation cost between empirical measures. Our proof is based on strengthening convergence results for dual solutions to the entropic optimal transport problem.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 31 of its 80 references that are in the map. First posted on arXiv 19 Apr 2022.

Builds on

31 of 80 references.

References · 31

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2018Computational Optimal Transportcited by 765
  3. 2015Optimal Transport for Domain Adaptationcited by 457
  4. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  5. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 182
  6. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 169
  7. 2018Gromov-Wasserstein Alignment of Word Embedding Spacescited by 119
  8. 2016Theoretical Analysis of Domain Adaptation with Optimal Transportcited by 105
  9. 2018Unsupervised Alignment of Embeddings with Wasserstein Procrustescited by 96
  10. 2021Entropic estimation of optimal transport mapscited by 87
  11. 2019Statistical bounds for entropic optimal transport: sample complexity and the central limit theoremcited by 85
  12. 2020Faster Wasserstein Distance Estimation with the Sinkhorn Divergencecited by 73
19 more
  1. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 67
  2. 2019FlipTest: Fairness Testing via Optimal Transportcited by 51
  3. 2020Entropy-Regularized 2-Wasserstein Distance between Gaussian Measurescited by 32
  4. 2021Entropic Optimal Transport: Convergence of Potentialscited by 30
  5. 2019Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithmcited by 27
  6. 2021Transport-based Counterfactual Modelscited by 27
  7. 2016Wasserstein Discriminant Analysiscited by 25
  8. 2021Stability of Entropic Optimal Transport and Schr"odinger Bridgescited by 25
  9. 2019Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportationcited by 24
  10. 2016Inference for Empirical Wasserstein Distances on Finite Spacescited by 21
  11. 2021Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithmcited by 21
  12. 2019Tackling Algorithmic Bias in Neural-Network Classifiers using Wasserstein-2 Regularizationcited by 18
  13. 2020The statistical effect of entropic regularization in optimal transportationcited by 14
  14. 2021Asymptotics for semi-discrete entropic optimal transportcited by 14
  15. 2022Stability of Schr"odinger Potentials and Convergence of Sinkhorn's Algorithmcited by 13
  16. 2018Uncoupled isotonic regression via minimum Wasserstein deconvolutioncited by 12
  17. 2020Multivariate goodness-of-Fit tests based on Wasserstein distancecited by 11
  18. 2021Fairness with Continuous Optimal Transportcited by 9
  19. 2021Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biologycited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 8; 2024: 4; 2025: 3; 2026: 1.

18 papers.

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  1. 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 29
  2. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  3. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  4. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  5. 2023Minimum intrinsic dimension scaling for entropic optimal transportcited by 11
  6. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  7. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  8. 2023Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approachcited by 7
  9. 2022Gaussian Processes on Distributions based on Regularized Optimal Transportcited by 6
  10. 2023Learning Elastic Costs to Shape Monge Displacementscited by 6
  11. 2024Distributional Counterfactual Explanations With Optimal Transportcited by 6
  12. 2024Diffeomorphic Measure Matching with Kernels for Generative Modelingcited by 4
6 more
  1. 2024Multivariate Stochastic Dominance via Optimal Transport and Applications to Models Benchmarkingcited by 2
  2. 2025Meta Optimality for Demographic Parity Constrained Regression via Post-Processingcited by 2
  3. 2023Improved learning theory for kernel distribution regression with two-stage samplingcited by 1
  4. 2025Leveraging Optimal Transport for Distributed Two-Sample Testing: An Integrated Transportation Distance-based Frameworkcited by 1
  5. 2025Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectivescited by 1
  6. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0