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Statistical Optimal Transport via Factored Couplings

arXiv 1806.07348 ↗First posted 19 Jun 2018stat.ML cs.LGcited by 38

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Abstract (arXiv)

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new structural assumption that is similar to the nonnegative rank of a matrix. Regularizing based on this assumption leads to drastic improvements on high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data. These findings are supported by a theoretical analysis that indicates that the transport rank is key in overcoming the curse of dimensionality inherent to data-driven optimal transport.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Jun 2018.

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Citing papers per year: 2021: 12; 2022: 4; 2023: 7; 2024: 3; 2025: 6; 2026: 6.

38 papers.

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  1. 2021Low-Rank Sinkhorn Factorizationcited by 66
  2. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  3. 2021Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costscited by 61
  4. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  5. 2022Meta Optimal Transportcited by 28
  6. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  7. 2022Low-rank Optimal Transport: Approximation, Statistics and Debiasingcited by 21
  8. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  9. 2021Martingale Methods for Sequential Estimation of Convex Functionals and Divergencescited by 17
  10. 2021A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regionscited by 17
  11. 2021Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and Morecited by 10
  12. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 8
26 more
  1. 2023Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approachcited by 7
  2. 2023Unbalanced Low-rank Optimal Transport Solverscited by 7
  3. 2021Improving Approximate Optimal Transport Distances using Quantizationcited by 5
  4. 2023Fast Optimal Transport through Sliced Wasserstein Generalized Geodesicscited by 5
  5. 2021Order Constraints in Optimal Transportcited by 4
  6. 2021Approximating Optimal Transport via Low-rank and Sparse Factorizationcited by 4
  7. 2021Matching for causal effects via multimarginal unbalanced optimal transportcited by 4
  8. 2022Tangential Wasserstein Projectionscited by 4
  9. 2023Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Spacecited by 4
  10. 2024Efficient approximation of Earth Mover's Distance Based on Nearest Neighbor Searchcited by 3
  11. 2021Factored couplings in multi-marginal optimal transport via difference of convex programmingcited by 2
  12. 2025Joint Metric Space Embedding by Unbalanced OT with Gromov-Wasserstein Marginal Penalizationcited by 2
  13. 2025Spherical Tree-Sliced Wasserstein Distancecited by 2
  14. 2022Budget-Constrained Bounds for Mini-Batch Estimation of Optimal Transportcited by 1
  15. 2024SAVA: Scalable Learning-Agnostic Data Valuationcited by 1
  16. 2024Optimal Transport for Probabilistic Circuitscited by 1
  17. 2025Fair Clustering via Alignmentcited by 1
  18. 2025Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectivescited by 1
  19. 2026A Riemannian Approach to Low-Rank Optimal Transportcited by 1
  20. 2021Efficient estimates of optimal transport via low-dimensional embeddingscited by 0
  21. 2025Simplifying Optimal Transport through Schatten-p Regularizationcited by 0
  22. 2026Transport Clustering: Solving Low-Rank Optimal Transport via Clusteringcited by 0
  23. 2026Supervised Distributional Reduction via Optimal Transport and Dependence Maximizationcited by 0
  24. 2026Cluster-Aware Matching via Laplacian Optimal Transportcited by 0
  25. 2026Exact Rank-Space KL Projection for Shared-Marginal Low-Rank Factors: Application to Doubly Stochastic Clusteringcited by 0
  26. 2026SinkSLOT: Sinkhorn via Sparse Lifted Optimal Transportcited by 0