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Sliced Wasserstein Kernels for Probability Distributions

arXiv 1511.03198 ↗First posted 10 Nov 2015cs.LG stat.MLcited by 65

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Abstract (arXiv)

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutions to the problem and has revamped its practical applications in machine learning. In this paper, we exploit the widely used kernel methods and provide a family of provably positive definite kernels based on the Sliced Wasserstein distance and demonstrate the benefits of these kernels in a variety of learning tasks. Our work provides a new perspective on the application of optimal transport flavored distances through kernel methods in machine learning tasks.

Key facts. Cited by 65 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Nov 2015.

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Citing papers per year: 2021: 16; 2022: 13; 2023: 11; 2024: 10; 2025: 9; 2026: 6.

65 papers.

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  1. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 125
  2. 2021Minibatch optimal transport distances; analysis and applicationscited by 65
  3. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  4. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 41
  5. 2021Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projectionscited by 33
  6. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  7. 2024An Aggregation-Free Federated Learning for Tackling Data Heterogeneitycited by 33
  8. 2022Meta Optimal Transportcited by 28
  9. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  10. 2022The Neural Process Family: Survey, Applications and Perspectivescited by 23
  11. 2022Sliced Optimal Partial Transportcited by 20
  12. 2023Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signalscited by 19
38 more
  1. 2021Diffusion Earth Mover's Distance and Distribution Embeddingscited by 18
  2. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  3. 2021Parametric Scattering Networkscited by 16
  4. 2023Unbalanced Optimal Transport: A Unified Framework for Object Detectioncited by 15
  5. 2022Improving GANs for Long-Tailed Data through Group Spectral Regularizationcited by 14
  6. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  7. 2021Re-evaluating Word Mover's Distancecited by 10
  8. 2025ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Planscited by 10
  9. 2021The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classificationcited by 9
  10. 2021SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddingscited by 9
  11. 2022Approximating 1-Wasserstein Distance with Treescited by 9
  12. 2022Nonlinear Sufficient Dimension Reduction for Distribution-on-Distribution Regressioncited by 8
  13. 2024Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variatescited by 8
  14. 2021Statistical and Topological Properties of Gaussian Smoothed Sliced Probability Divergencescited by 7
  15. 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
  16. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  17. 2024Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernelscited by 7
  18. 2022Gaussian Processes on Distributions based on Regularized Optimal Transportcited by 6
  19. 2022Universal Neural Optimal Transportcited by 6
  20. 2023Scalable Counterfactual Distribution Estimation in Multivariate Causal Modelscited by 6
  21. 2022Partial Wasserstein Adversarial Network for Non-rigid Point Set Registrationcited by 5
  22. 2021Iterative Alignment Flowscited by 4
  23. 2023SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamicscited by 4
  24. 2024WeiPer: OOD Detection using Weight Perturbations of Class Projectionscited by 4
  25. 2025Fast rigid alignment of heterogeneous images in sliced Wasserstein distancecited by 4
  26. 2024Learning to Embed Distributions via Maximum Kernel Entropycited by 3
  27. 2022Mitigating Closed-model Adversarial Examples with Bayesian Neural Modeling for Enhanced End-to-End Speech Recognitioncited by 2
  28. 2023PTLp: Partial Transport Lp Distancescited by 2
  29. 2023Partial Transport for Point-Cloud Registrationcited by 2
  30. 2025Constrained Sliced Wasserstein Embeddingcited by 2
  31. 2026Sinkhorn doubly stochastic attention rank decay analysiscited by 2
  32. 2021Separation Results between Fixed-Kernel and Feature-Learning Probability Metricscited by 1
  33. 2021Rethinking Multidimensional Discriminator Output for Generative Adversarial Networkscited by 1
  34. 2022Budget-Constrained Bounds for Mini-Batch Estimation of Optimal Transportcited by 1
  35. 2023Improved learning theory for kernel distribution regression with two-stage samplingcited by 1
  36. 2024Continuous Unsupervised Domain Adaptation Using Stabilized Representations and Experience Replaycited by 1
  37. 2024Fast unsupervised ground metric learning with tree-Wasserstein distancecited by 1
  38. 2025Unbiased Sliced Wasserstein Kernels for High-Quality Audio Captioningcited by 1

50 most cited of 65 All 65 (JSON)