mlsanityData to 14 Oct 2026

Order Constraints in Optimal Transport

arXiv 2110.07275 ↗First posted 14 Oct 2021cs.LG cs.AIcited by 4

Not on the map. Why?

Abstract (arXiv)

Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure. We introduce novel order constraints into the optimal transport formulation to allow for the incorporation of structure. We define an efficient method for obtaining explainable solutions to the new formulation that scales far better than standard approaches. The theoretical properties of the method are provided. We demonstrate experimentally that order constraints improve explainability using the e-SNLI (Stanford Natural Language Inference) dataset that includes human-annotated rationales as well as on several image color transfer examples.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 32 of its 59 references that are in the map. First posted on arXiv 14 Oct 2021.

Builds on

32 of 59 references.

References · 32

  1. 2021Convex optimizationcited by 2,515
  2. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  3. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,355
  4. 2018e-SNLI: Natural Language Inference with Natural Language Explanationscited by 468
  5. 2015Optimal Transport for Domain Adaptationcited by 463
  6. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 223
  7. 2019One Explanation Does Not Fit All: A Toolkit and Taxonomy of AI Explainability Techniquescited by 164
  8. 2019Optimal Feature Transport for Cross-View Image Geo-Localizationcited by 91
  9. 2017Smooth and Sparse Optimal Transportcited by 83
  10. 2016Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problemscited by 73
  11. 2021Low-Rank Sinkhorn Factorizationcited by 67
  12. 2019On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithmscited by 62
20 more
  1. 2019Hierarchical Optimal Transport for Document Representationcited by 53
  2. 2014Multi-marginal optimal transport: theory and applicationscited by 41
  3. 2018Massively scalable Sinkhorn distances via the Nystr"om methodcited by 41
  4. 2018Statistical Optimal Transport via Factored Couplingscited by 38
  5. 2020All of the Fairness for Edge Prediction with Optimal Transportcited by 36
  6. 2020On Projection Robust Optimal Transport: Sample Complexity and Model Misspecificationcited by 34
  7. 2018Towards Optimal Transport with Global Invariancescited by 33
  8. 2017Structured Optimal Transportcited by 31
  9. 2018Word Mover's Embedding: From Word2Vec to Document Embeddingcited by 26
  10. 2020Rationalizing Text Matching: Learning Sparse Alignments via Optimal Transportcited by 20
  11. 2019Regularity as Regularization: Smooth and Strongly Convex Brenier Potentials in Optimal Transportcited by 19
  12. 2019On a Combination of Alternating Minimization and Nesterov's Momentumcited by 18
  13. 2018Optimal Transport on Discrete Domainscited by 16
  14. 2020Polynomial-time algorithms for Multimarginal Optimal Transport problems with structurecited by 15
  15. 2019Unsupervised Hierarchy Matching with Optimal Transport over Hyperbolic Spacescited by 14
  16. 2020Hardness results for Multimarginal Optimal Transport problemscited by 13
  17. 2017Dykstra's Algorithm, ADMM, and Coordinate Descent: Connections, Insights, and Extensionscited by 12
  18. 2018Context Mover's Distance & Barycenters: Optimal Transport of Contexts for Building Representationscited by 11
  19. 2021Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samplescited by 8
  20. 2015Optimal Transportation Theory with Repulsive Costscited by 5

Built on by

Cited by year (2026 to 14 Oct)

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

4 papers.

  1. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  2. 2023Timestamp-supervised Wearable-based Activity Segmentation and Recognition with Contrastive Learning and Order-Preserving Optimal Transportcited by 10
  3. 2025Many-to-Many Matching via Sparsity Controlled Optimal Transportcited by 0
  4. 2026From Cone Geometry to Monge Structure: Local Defects and Global Regret in High-Dimensional Optimal Transportcited by 0