mlsanityData to 7 Oct 2026

Measure transfer via stochastic slicing and matching

arXiv 2307.05705 ↗First posted 11 Jul 2023math.NA cs.NA math.STcited by 6

Not on the map. Why?

Abstract (arXiv)

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of closed-form solutions for the one-dimensional optimal transport problem and the associated computational advantages. While such schemes have already been successfully utilized in data science applications, not too many results on their convergence are available. The main contribution of this paper is an almost sure convergence proof for stochastic slicing-and-matching schemes. The proof builds on an interpretation as a stochastic gradient descent scheme on the Wasserstein space. Numerical examples on step-wise image morphing are demonstrated as well.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 19 of its 68 references that are in the map. First posted on arXiv 11 Jul 2023.

Builds on

19 of 68 references.

References · 19

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2019Generalized Sliced Wasserstein Distancescited by 205
  3. 2015Learning with a Wasserstein Losscited by 194
  4. 2018Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusionscited by 77
  5. 2020On the representation and learning of monotone triangular transport mapscited by 41
  6. 2020Sliced Iterative Normalizing Flowscited by 37
  7. 2020Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbationscited by 37
  8. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  9. 2015The Cumulative Distribution Transform and Linear Pattern Classificationcited by 19
  10. 2022Sliced Optimal Partial Transportcited by 19
  11. 2017Fr'echet Means and Procrustes Analysis in Wasserstein Spacecited by 18
  12. 2021Large-scale optimal transport map estimation using projection pursuitcited by 16
7 more
  1. 2020Partitioning signal classes using transport transforms for data analysis and machine learningcited by 15
  2. 2022Supervised learning of sheared distributions using linearized optimal transportcited by 14
  3. 2023Slicing Unbalanced Optimal Transportcited by 10
  4. 2023Applications of No-Collision Transportation Maps in Manifold Learningcited by 6
  5. 2019No-collision Transportation Mapscited by 5
  6. 2023Fast Optimal Transport through Sliced Wasserstein Generalized Geodesicscited by 5
  7. 2022Stochastic Gradient Descent for Barycenters in Wasserstein Spacecited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 1; 2026: 2.

6 papers.

  1. 2023Conditional Optimal Transport on Function Spacescited by 26
  2. 2023Approximation properties of slice-matching operatorscited by 3
  3. 2025Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysiscited by 3
  4. 2023Partial Transport for Point-Cloud Registrationcited by 2
  5. 2026Convergence Rates for Distribution Matching with Sliced Optimal Transportcited by 2
  6. 2026Distribution Steering via Sliced Optimal Transport Controlcited by 0