mlsanityData to 7 Oct 2026

Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances

arXiv 2206.03230 ↗First posted 7 Jun 2022stat.ML cs.LGcited by 7

Not on the map. Why?

Abstract (arXiv)

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties -- with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 41 of its 74 references that are in the map. First posted on arXiv 7 Jun 2022.

Builds on

41 of 74 references.

References · 41

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29 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 1; 2025: 1; 2026: 1.

7 papers.

  1. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  2. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  3. 2023PAC-Bayesian Generalization Bounds for Adversarial Generative Modelscited by 13
  4. 2023Wasserstein PAC-Bayes Learning: Exploiting Optimisation Guarantees to Explain Generalisationcited by 3
  5. 2024Towards Better Spherical Sliced-Wasserstein Distance Learning with Data-Adaptive Discriminative Projection Directioncited by 1
  6. 2025Minimax-Optimal Two-Sample Test with Sliced Wassersteincited by 1
  7. 2026Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functionscited by 0