mlsanityData to 7 Oct 2026

Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem

arXiv 1905.11882 ↗First posted 28 May 2019math.ST cs.LG stat.MLcited by 85

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Abstract (arXiv)

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of convergence of entropic OT for empirical measures. Our analysis improves exponentially on the bound of Genevay et al. (2019) and extends their work to unbounded measures. Second, we establish a central limit theorem for entropic OT, based on techniques developed by Del Barrio and Loubes (2019). Previously, such a result was only known for finite metric spaces. As an application of our results, we develop and analyze a new technique for estimating the entropy of a random variable corrupted by gaussian noise.

Key facts. Cited by 85 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 May 2019.

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Citing papers per year: 2021: 17; 2022: 15; 2023: 20; 2024: 13; 2025: 8; 2026: 12.

85 papers.

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  1. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 96
  2. 2021Entropic estimation of optimal transport mapscited by 87
  3. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  4. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  5. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  6. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  7. 2023The Monge Gap: A Regularizer to Learn All Transport Mapscited by 32
  8. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  9. 2024Wasserstein Flow Matching: Generative modeling over families of distributionscited by 27
  10. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  11. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  12. 2022Hierarchical Sliced Wasserstein Distancecited by 23
38 more
  1. 2022Low-rank Optimal Transport: Approximation, Statistics and Debiasingcited by 21
  2. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  3. 2022Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metricscited by 18
  4. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  5. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  6. 2023Projected Langevin dynamics and a gradient flow for entropic optimal transportcited by 17
  7. 2021Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applicationscited by 15
  8. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  9. 2021Entropy Partial Transport with Tree Metrics: Theory and Practicecited by 13
  10. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  11. 2023Minimum intrinsic dimension scaling for entropic optimal transportcited by 11
  12. 2023Sample Complexity Bounds for Estimating Probability Divergences under Invariancescited by 11
  13. 2023Scalable Unbalanced Sobolev Transport for Measures on a Graphcited by 10
  14. 2024Progressive Entropic Optimal Transport Solverscited by 10
  15. 2025On Fitting Flow Models with Large Sinkhorn Couplingscited by 10
  16. 2021Entropy Regularized Optimal Transport Independence Criterioncited by 9
  17. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
  18. 2024Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier mapscited by 9
  19. 2021Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samplescited by 8
  20. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  21. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  22. 2021Optimal transport weights for causal inferencecited by 7
  23. 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
  24. 2023Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstructioncited by 7
  25. 2023Unbalanced Low-rank Optimal Transport Solverscited by 7
  26. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  27. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  28. 2021Understanding Entropic Regularization in GANscited by 6
  29. 2022Gaussian Processes on Distributions based on Regularized Optimal Transportcited by 6
  30. 2021Unsupervised Ground Metric Learning using Wasserstein Singular Vectorscited by 5
  31. 2021Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transportcited by 5
  32. 2023Estimating the Rate-Distortion Function by Wasserstein Gradient Descentcited by 5
  33. 2021Multivariate rank via entropic optimal transport: sample efficiency and generative modelingcited by 4
  34. 2024A Universal Metric of Dataset Similarity for Cross-silo Federated Learningcited by 4
  35. 2024Robust Generative Learning with Lipschitz-Regularized α-Divergences Allows Minimal Assumptions on Target Distributionscited by 4
  36. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4
  37. 2021Convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settingscited by 3
  38. 2022Entropic Optimal Transport in Random Graphscited by 3

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