mlsanityData to 7 Oct 2026

Sharp bounds for max-sliced Wasserstein distances

arXiv 2403.00666 ↗First posted 1 Mar 2024math.PR stat.MLcited by 10

Not on the map. Why?

Abstract (arXiv)

We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from n samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure μ on a Euclidean space and its symmetrized empirical distribution in terms of the operator norm of the covariance matrix of μ and the diameter of the support of μ.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 17 of its 51 references that are in the map. First posted on arXiv 1 Mar 2024.

Builds on

17 of 51 references.

References · 17

  1. 2015An Introduction to Matrix Concentration Inequalitiescited by 391
  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. 2017Sliced Wasserstein Kernel for Persistence Diagramscited by 77
  7. 2019Sliced Wasserstein Generative Modelscited by 61
  8. 2020Projection Robust Wasserstein Distance and Riemannian Optimizationcited by 45
  9. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  10. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  11. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  12. 2020On Projection Robust Optimal Transport: Sample Complexity and Model Misspecificationcited by 34
5 more
  1. 2022Spherical Sliced-Wassersteincited by 31
  2. 2020Two-sample Test using Projected Wasserstein Distancecited by 17
  3. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  4. 2022Covariance Estimation: Optimal Dimension-free Guarantees for Adversarial Corruption and Heavy Tailscited by 14
  5. 2022The out-of-sample prediction error of the square-root-LASSO and related estimatorscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 3; 2026: 3.

10 papers.

  1. 2025Lightspeed Geometric Dataset Distance via Sliced Optimal Transportcited by 10
  2. 2024Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distancescited by 4
  3. 2024Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixturescited by 4
  4. 2024Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHScited by 1
  5. 2025Minimax-Optimal Two-Sample Test with Sliced Wassersteincited by 1
  6. 2026Bayesian Multiple Multivariate Density-Density Regressioncited by 1
  7. 2026Sliced Inner Product Gromov-Wasserstein Distancescited by 1
  8. 2024Max-sliced 2-Wasserstein distancecited by 0
  9. 2025Streaming Sliced Optimal Transportcited by 0
  10. 2026Revisiting the Sliced Wasserstein Kernel for persistence diagrams: a Figalli-Gigli approachcited by 0