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Orthogonal Estimation of Wasserstein Distances

arXiv 1903.03784 ↗First posted 9 Mar 2019stat.ML cs.LGcited by 32

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Abstract (arXiv)

Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling, and evaluate our approaches experimentally in a range of large-scale experiments in generative modelling and reinforcement learning.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Mar 2019.

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Citing papers per year: 2021: 6; 2022: 5; 2023: 7; 2024: 2; 2025: 7; 2026: 5.

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  1. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  2. 2021On the Expressive Power of Self-Attention Matricescited by 47
  3. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  4. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  5. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  6. 2021Wasserstein Unsupervised Reinforcement Learningcited by 22
  7. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  8. 2024Expected Sliced Transport Planscited by 19
  9. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  10. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  11. 2022Hilbert Curve Projection Distance for Distribution Comparisoncited by 9
  12. 2023Scalable Infomin Learningcited by 8
20 more
  1. 2026Image Generation with a Sphere Encodercited by 8
  2. 2025A User's Guide to Sampling Strategies for Sliced Optimal Transportcited by 7
  3. 2023Repelling Random Walkscited by 6
  4. 2021Sliced Multi-Marginal Optimal Transportcited by 5
  5. 2023Fast Optimal Transport through Sliced Wasserstein Generalized Geodesicscited by 5
  6. 2025Task Adaptation from Skills: Information Geometry, Disentanglement, and New Objectives for Unsupervised Reinforcement Learningcited by 5
  7. 2025Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distancescited by 5
  8. 2025Efficient Transferable Optimal Transport via Min-Sliced Transport Planscited by 4
  9. 2024Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equationscited by 3
  10. 2025Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysiscited by 3
  11. 2023Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networkscited by 2
  12. 2026Sliced-Regularized Optimal Transportcited by 2
  13. 2021Heterogeneous Wasserstein Discrepancy for Incomparable Distributionscited by 1
  14. 2022A Simple Way to Learn Metrics Between Attributed Graphscited by 1
  15. 2025Keep your distance: learning dispersed embeddings on mathbbSmcited by 1
  16. 2025Repulsive Monte Carlo on the sphere for the sliced Wasserstein distancecited by 1
  17. 2023Wasserstein Diversity-Enriched Regularizer for Hierarchical Reinforcement Learningcited by 0
  18. 2026Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wassersteincited by 0
  19. 2026Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functionscited by 0
  20. 2026SinkSLOT: Sinkhorn via Sparse Lifted Optimal Transportcited by 0