mlsanityData to 14 Oct 2026

Learning with a Wasserstein Loss

arXiv 1506.05439 ↗First posted 17 Jun 2015cs.LG cs.CV stat.MLcited by 196

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Abstract (arXiv)

Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe an efficient learning algorithm based on this regularization, as well as a novel extension of the Wasserstein distance from probability measures to unnormalized measures. We also describe a statistical learning bound for the loss. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data tag prediction problem, using the Yahoo Flickr Creative Commons dataset, outperforming a baseline that doesn't use the metric.

Key facts. Cited by 196 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Jun 2015.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 34; 2022: 41; 2023: 42; 2024: 34; 2025: 25; 2026: 19.

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  1. 2023Multimodal Optimal Transport-based Co-Attention Transformer with Global Structure Consistency for Survival Predictioncited by 86
  2. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  3. 2021Minibatch optimal transport distances; analysis and applicationscited by 65
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  10. 2023Convolutional Cross-View Pose Estimationcited by 36
  11. 2022DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualizationcited by 32
  12. 2024Improving Diffusion-Based Image Synthesis with Context Predictioncited by 32
38 more
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  5. 2021Semi-Supervised Multi-Modal Multi-Instance Multi-Label Deep Network with Optimal Transportcited by 28
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  7. 2022A Unified Framework for Implicit Sinkhorn Differentiationcited by 28
  8. 2022Meta Optimal Transportcited by 28
  9. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 28
  10. 2024Addressing Misspecification in Simulation-based Inference through Data-driven Calibrationcited by 27
  11. 2023Pre-training for Speech Translation: CTC Meets Optimal Transportcited by 25
  12. 2022Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfecited by 22
  13. 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
  14. 2023PatchCT: Aligning Patch Set and Label Set with Conditional Transport for Multi-Label Image Classificationcited by 21
  15. 2022Sliced Optimal Partial Transportcited by 20
  16. 2022Implicit Graphon Neural Representationcited by 19
  17. 2023SOOD: Towards Semi-Supervised Oriented Object Detectioncited by 19
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  20. 2022Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplingscited by 17
  21. 2023Counterfactual Generative Models for Time-Varying Treatmentscited by 17
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  23. 2022On Unbalanced Optimal Transport: Gradient Methods, Sparsity and Approximation Errorcited by 16
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  26. 2024Sinkhorn Distance Minimization for Knowledge Distillationcited by 15
  27. 2021Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learningcited by 14
  28. 2024Pushing the Limits of Zero-shot End-to-End Speech Translationcited by 14
  29. 2021Entropy Partial Transport with Tree Metrics: Theory and Practicecited by 13
  30. 2021SPOT: A framework for selection of prototypes using optimal transportcited by 13
  31. 2022Unsupervised Model Adaptation for Source-free Segmentation of Medical Imagescited by 13
  32. 2022Modeling Multimodal Aleatoric Uncertainty in Segmentation with Mixture of Stochastic Expertscited by 13
  33. 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldscited by 13
  34. 2024P2OT: Progressive Partial Optimal Transport for Deep Imbalanced Clusteringcited by 13
  35. 2022Optimal Transport of Classifiers to Fairnesscited by 12
  36. 2024SOOD++: Leveraging Unlabeled Data to Boost Oriented Object Detectioncited by 12
  37. 2025Discovering Fine-Grained Visual-Concept Relations by Disentangled Optimal Transport Concept Bottleneck Modelscited by 12
  38. 2021Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and Morecited by 11

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