mlsanityData to 7 Oct 2026

Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances

arXiv 2210.09160 ↗First posted 17 Oct 2022stat.ML cs.LGcited by 41

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Abstract (arXiv)

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i) empirical convergence rates; (ii) robustness to data contamination; and (iii) efficient computational methods. For empirical convergence, we derive fast rates with explicit dependence of constants on dimension, subject to log-concavity of the population distributions. For robustness, we characterize minimax optimal, dimension-free robust estimation risks, and show an equivalence between robust sliced 1-Wasserstein estimation and robust mean estimation. This enables lifting statistical and algorithmic guarantees available for the latter to the sliced 1-Wasserstein setting. Moving on to computational aspects, we analyze the Monte Carlo estimator for the average-sliced distance, demonstrating that larger dimension can result in faster convergence of the numerical integration error. For the max-sliced distance, we focus on a subgradient-based local optimization algorithm that is frequently used in practice, albeit without formal guarantees, and establish an O(ε-4) computational complexity bound for it. Our theory is validated by numerical experiments, which altogether provide a comprehensive quantitative account of the scalability question.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). Builds on 26 of its 66 references that are in the map. First posted on arXiv 17 Oct 2022.

Builds on

26 of 66 references.

References · 26

  1. 2017Improved Training of Wasserstein GANscited by 2,223
  2. 2019Generalized Sliced Wasserstein Distancescited by 205
  3. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 118
  4. 2018Generative Modeling using the Sliced Wasserstein Distancecited by 108
  5. 2019Subspace Robust Wasserstein Distancescited by 89
  6. 2020Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptationcited by 86
  7. 2017Being Robust (in High Dimensions) Can Be Practicalcited by 83
  8. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
  9. 2017Sliced Wasserstein Kernel for Persistence Diagramscited by 77
  10. 2019Sliced Wasserstein Generative Modelscited by 61
  11. 2020Projection Robust Wasserstein Distance and Riemannian Optimizationcited by 45
  12. 2020Outlier-Robust Optimal Transportcited by 45
14 more
  1. 2020Robust and Heavy-Tailed Mean Estimation Made Simple, via Regret Minimizationcited by 44
  2. 2017Resilience: A Criterion for Learning in the Presence of Arbitrary Outlierscited by 43
  3. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  4. 2017Global optimization of Lipschitz functionscited by 39
  5. 2019Generalized Resilience and Robust Statisticscited by 37
  6. 2020On Projection Robust Optimal Transport: Sample Complexity and Model Misspecificationcited by 34
  7. 2021Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projectionscited by 33
  8. 2018Stochastic subgradient method converges at the rate O(k-1/4) on weakly convex functionscited by 31
  9. 2020A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distancecited by 27
  10. 2021Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysiscited by 27
  11. 2019Minimax Confidence Intervals for the Sliced Wasserstein Distancecited by 24
  12. 2020When OT meets MoM: Robust estimation of Wasserstein Distancecited by 23
  13. 2019Approximate Bayesian Computation with the Sliced-Wasserstein Distancecited by 22
  14. 2021Differentially Private Sliced Wasserstein Distancecited by 19

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Citing papers per year: 2023: 8; 2024: 12; 2025: 12; 2026: 9.

41 papers.

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  1. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  2. 2024Sliced Wasserstein with Random-Path Projecting Directionscited by 15
  3. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  4. 2023Max-Sliced Mutual Informationcited by 10
  5. 2024Sharp bounds for max-sliced Wasserstein distancescited by 10
  6. 2025Lightspeed Geometric Dataset Distance via Sliced Optimal Transportcited by 10
  7. 2024Deep Structural Knowledge Exploitation and Synergy for Estimating Node Importance Value on Heterogeneous Information Networkscited by 9
  8. 2023Robust Estimation under the Wasserstein Distancecited by 8
  9. 2024Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variatescited by 8
  10. 2024Time-Causal VAE: Robust Financial Time Series Generatorcited by 8
  11. 2023Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstructioncited by 7
  12. 2024Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernelscited by 7
29 more
  1. 2024Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributionscited by 6
  2. 2024Robust Distribution Learning with Local and Global Adversarial Corruptionscited by 5
  3. 2025Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distancescited by 5
  4. 2026QQWorld: Quantile-Quantile Matching for World Model Regularizationcited by 5
  5. 2023Convergence of SGD for Training Neural Networks with Sliced Wasserstein Lossescited by 4
  6. 2024Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distancescited by 4
  7. 2025Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysiscited by 3
  8. 2023Probabilistic Constrained Reinforcement Learning with Formal Interpretabilitycited by 1
  9. 2024Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHScited by 1
  10. 2024Towards Better Spherical Sliced-Wasserstein Distance Learning with Data-Adaptive Discriminative Projection Directioncited by 1
  11. 2025Unbiased Sliced Wasserstein Kernels for High-Quality Audio Captioningcited by 1
  12. 2025Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate datacited by 1
  13. 2025Distributional encoding for Gaussian process regression with qualitative inputscited by 1
  14. 2025Robust Alignment via Partial Gromov-Wasserstein Distancescited by 1
  15. 2025Minimax-Optimal Two-Sample Test with Sliced Wassersteincited by 1
  16. 2026Detecting Performance Degradation under Data Shift in Pathology Vision-Language Modelcited by 1
  17. 2026Bayesian Multiple Multivariate Density-Density Regressioncited by 1
  18. 2026Sliced Inner Product Gromov-Wasserstein Distancescited by 1
  19. 2023Reconstruction of dynamical systems from data without time labelscited by 0
  20. 2024A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagramscited by 0
  21. 2025Overlap-Aware Feature Learning for Robust Unsupervised Domain Adaptation for 3D Semantic Segmentationcited by 0
  22. 2025Streaming Sliced Optimal Transportcited by 0
  23. 2025Relation-Aware Slicing in Cross-Domain Alignmentcited by 0
  24. 2025Population synthesis with geographic coordinatescited by 0
  25. 2026Approximating f-Divergences with Rank Statisticscited by 0
  26. 2026The Observable Wasserstein Distancecited by 0
  27. 2026Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functionscited by 0
  28. 2026High-Dimensional Online Change Point Detection with Adaptive Thresholding and Interpretabilitycited by 0
  29. 2026LAYERSCOPE: A Layerwise Characterization of Video and Multimodal Learned Representationscited by 0