mlsanityData to 7 Oct 2026

Inference for Empirical Wasserstein Distances on Finite Spaces

arXiv 1610.03287 ↗First posted 11 Oct 2016stat.MEcited by 21

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Abstract (arXiv)

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic distribution of empirical Wasserstein distances as the optimal value of a linear program with random objective function. This facilitates statistical inference (e.g. confidence intervals for sample based Wasserstein distances) in large generality. Our proof is based on directional Hadamard differentiability. Failure of the classical bootstrap and alternatives are discussed. The utility of the distributional results is illustrated on two data sets.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Oct 2016.

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Citing papers per year: 2021: 10; 2022: 3; 2023: 3; 2024: 1; 2025: 2; 2026: 2.

21 papers.

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  1. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 67
  2. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  3. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  4. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  5. 2021Martingale Methods for Sequential Estimation of Convex Functionals and Divergencescited by 17
  6. 2021Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applicationscited by 15
  7. 2021Entropy Partial Transport with Tree Metrics: Theory and Practicecited by 13
  8. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  9. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  10. 2021The Gene Mover's Distance: Single-cell similarity via Optimal Transportcited by 8
  11. 2021Optimal transport weights for causal inferencecited by 7
  12. 2022Estimation and inference for the Wasserstein distance between mixing measures in topic modelscited by 4
9 more
  1. 2021Likelihood estimation of sparse topic distributions in topic models and its applications to Wasserstein document distance calculationscited by 2
  2. 2021Limit Distribution Theory for the Smooth 1-Wasserstein Distance with Applicationscited by 1
  3. 2023A Specialized Semismooth Newton Method for Kernel-Based Optimal Transportcited by 1
  4. 2025Network Embedding Exploration Tool (NEExT)cited by 1
  5. 2025Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectivescited by 1
  6. 2021Estimation of Stationary Optimal Transport Planscited by 0
  7. 2024Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spacescited by 0
  8. 2026Statistical Guarantees for Reasoning Probes on Looped Boolean Circuitscited by 0
  9. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0