mlsanityData to 7 Oct 2026

Outlier-Robust Optimal Transport

arXiv 2012.07363 ↗First posted 14 Dec 2020stat.MEcited by 45

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Abstract (arXiv)

Optimal transport (OT) measures distances between distributions in a way that depends on the geometry of the sample space. In light of recent advances in computational OT, OT distances are widely used as loss functions in machine learning. Despite their prevalence and advantages, OT loss functions can be extremely sensitive to outliers. In fact, a single adversarially-picked outlier can increase the standard W2-distance arbitrarily. To address this issue, we propose an outlier-robust formulation of OT. Our formulation is convex but challenging to scale at a first glance. Our main contribution is deriving an equivalent formulation based on cost truncation that is easy to incorporate into modern algorithms for computational OT. We demonstrate the benefits of our formulation in mean estimation problems under the Huber contamination model in simulations and outlier detection tasks on real data.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Dec 2020.

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Citing papers per year: 2021: 8; 2022: 9; 2023: 10; 2024: 8; 2025: 6; 2026: 4.

45 papers.

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  1. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  2. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  3. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  4. 2021Accurate Point Cloud Registration with Robust Optimal Transportcited by 38
  5. 2021Unbalanced Optimal Transport through Non-negative Penalized Linear Regressioncited by 31
  6. 2021On Robust Optimal Transport: Computational Complexity and Barycenter Computationcited by 27
  7. 2021Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysiscited by 27
  8. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  9. 2022Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfecited by 22
  10. 2022Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metricscited by 18
  11. 2021A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regionscited by 17
  12. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
33 more
  1. 2023Scalable Unbalanced Sobolev Transport for Measures on a Graphcited by 10
  2. 2022Hilbert Curve Projection Distance for Distribution Comparisoncited by 9
  3. 2022InfoOT: Information Maximizing Optimal Transportcited by 9
  4. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
  5. 2023Robust Estimation under the Wasserstein Distancecited by 8
  6. 2021Functional optimal transport: map estimation and domain adaptation for functional datacited by 7
  7. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  8. 2024A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributionscited by 7
  9. 2022Unbalanced CO-Optimal Transportcited by 6
  10. 2023Outlier-Robust Gromov-Wasserstein for Graph Datacited by 6
  11. 2024Robust Distribution Learning with Local and Global Adversarial Corruptionscited by 5
  12. 2025Robust Distribution Alignment for Industrial Anomaly Detection under Distribution Shiftcited by 5
  13. 2021Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distancecited by 4
  14. 2024Approximate Algorithms For k-Sparse Wasserstein Barycenter With Outlierscited by 3
  15. 2024Relative Translation Invariant Wasserstein Distancecited by 3
  16. 2022A Data-dependent Approach for High Dimensional (Robust) Wasserstein Alignmentcited by 2
  17. 2023Inference via robust optimal transportation: theory and methodscited by 2
  18. 2025Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomenacited by 2
  19. 2023Keypoint-Guided Optimal Transport: Models, Algorithms, and Applicationscited by 1
  20. 2023Computing the Distance between unbalanced Distributions -- The flat Metriccited by 1
  21. 2023Optimal Transport with Adaptive Regularisationcited by 1
  22. 2024Feature Selection via Maximizing Distances between Class Conditional Distributionscited by 1
  23. 2024Partial Distribution Matching via Partial Wasserstein Adversarial Networkscited by 1
  24. 2025Robust Alignment via Partial Gromov-Wasserstein Distancescited by 1
  25. 2022Robust computation of optimal transport by β-potential regularizationcited by 0
  26. 2024On the Shape of Brainscores for Large Language Models (LLMs)cited by 0
  27. 2025An Efficient Orlicz-Sobolev Approach for Transporting Unbalanced Measures on a Graphcited by 0
  28. 2025Partial Distribution Alignment via Adaptive Optimal Transportcited by 0
  29. 2025E-ROBOT: a dimension-free method for robust statistics and machine learning via Schr"odinger bridgecited by 0
  30. 2026Robust OT-Guided Generative Residual Domain Adaptation for Bike-Sharing Demand Prediction under Temporal Domain Shiftcited by 0
  31. 2026Wasserstein Filtering: A Sample Selection Method for Robust Distribution Learningcited by 0
  32. 2026Coupled Optimal Transport with Landmark Constraintscited by 0
  33. 2026Distributionally Robust Schr"odinger Bridgecited by 0