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Large-Scale Optimal Transport and Mapping Estimation

arXiv 1711.02283 ↗First posted 7 Nov 2017stat.MLcited by 120

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Abstract (arXiv)

This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two distributions. To that end, we propose a stochastic dual approach of regularized OT, and show empirically that it scales better than a recent related approach when the amount of samples is very large. Second, we estimate a textitMonge map as a deep neural network learned by approximating the barycentric projection of the previously-obtained OT plan. This parameterization allows generalization of the mapping outside the support of the input measure. We prove two theoretical stability results of regularized OT which show that our estimations converge to the OT plan and Monge map between the underlying continuous measures. We showcase our proposed approach on two applications: domain adaptation and generative modeling.

Key facts. Cited by 120 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Nov 2017.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 25; 2022: 18; 2023: 29; 2024: 21; 2025: 18; 2026: 8.

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  1. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  2. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  3. 2022Neural Optimal Transportcited by 123
  4. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  5. 2021Entropic estimation of optimal transport mapscited by 87
  6. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  7. 2021Generative Modeling with Optimal Transport Mapscited by 80
  8. 2021Large-Scale Wasserstein Gradient Flowscited by 76
  9. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  10. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  11. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  12. 2019Wasserstein Adversarial Imitation Learningcited by 59
38 more
  1. 2021Differentiable Particle Filtering via Entropy-Regularized Optimal Transportcited by 59
  2. 2021Score-based Generative Neural Networks for Large-Scale Optimal Transportcited by 59
  3. 2021Variational Wasserstein gradient flowcited by 53
  4. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  5. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 50
  6. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  7. 2024Light and Optimal Schr"odinger Bridge Matchingcited by 45
  8. 2021Neural Monge Map estimation and its applicationscited by 40
  9. 2023Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transportcited by 39
  10. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  11. 2023Optimal Transport for Treatment Effect Estimationcited by 32
  12. 2022Kernel Neural Optimal Transportcited by 31
  13. 2022On amortizing convex conjugates for optimal transportcited by 30
  14. 2022Meta Optimal Transportcited by 28
  15. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  16. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  17. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  18. 2022Wasserstein Iterative Networks for Barycenter Estimationcited by 23
  19. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  20. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  21. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19
  22. 2023Light Schr"odinger Bridgecited by 18
  23. 2021Large-scale optimal transport map estimation using projection pursuitcited by 16
  24. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  25. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  26. 2021Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solutioncited by 13
  27. 2023Causal Optimal Transport of Abstractionscited by 13
  28. 2021Near-optimal estimation of smooth transport maps with kernel sums-of-squarescited by 12
  29. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
  30. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 12
  31. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  32. 2024Adversarial Schr"odinger Bridge Matchingcited by 12
  33. 2023Minimum intrinsic dimension scaling for entropic optimal transportcited by 11
  34. 2023Optimal Transport-Guided Conditional Score-Based Diffusion Modelscited by 11
  35. 2021Learning High Dimensional Wasserstein Geodesicscited by 10
  36. 2024Graph Edit Distance with General Costs Using Neural Set Divergencecited by 10
  37. 2024Neural Topic Modeling with Large Language Models in the Loopcited by 10
  38. 2021Fairness with Continuous Optimal Transportcited by 9

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