mlsanityData to 7 Oct 2026

Centered plug-in estimation of Wasserstein distances

arXiv 2203.11627 ↗First posted 22 Mar 2022stat.ML stat.CO stat.MEcited by 2

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Abstract (arXiv)

The plug-in estimator of the squared Euclidean 2-Wasserstein distance is conservative, however due to its large positive bias it is often uninformative. We eliminate most of this bias using a simple centering procedure based on linear combinations. We construct a pair of centered plug-in estimators that decrease with the true Wasserstein distance, and are therefore guaranteed to be informative, for any finite sample size. Crucially, we demonstrate that these estimators can often be viewed as complementary upper and lower bounds on the squared Wasserstein distance. Finally, we apply the estimators to Bayesian computation, developing methods for estimating (i) the bias of approximate inference methods and (ii) the convergence of MCMC algorithms.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 27 of its 106 references that are in the map. First posted on arXiv 22 Mar 2022.

Builds on

27 of 106 references.

References · 27

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  2. 2016Variational Inference: A Review for Statisticianscited by 1,466
  3. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  4. 2018Statistical Aspects of Wasserstein Distancescited by 202
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  11. 2020Kernel Operations on the GPU, with Autodiff, without Memory Overflowscited by 101
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15 more
  1. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 67
  2. 2019Stochastic gradient Markov chain Monte Carlocited by 56
  3. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  4. 2015On Markov chain Monte Carlo methods for tall datacited by 50
  5. 2018On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradientcited by 42
  6. 2019Validated Variational Inference via Practical Posterior Error Boundscited by 26
  7. 2017Control Variates for Stochastic Gradient MCMCcited by 25
  8. 2022Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfecited by 22
  9. 2019Regularity as Regularization: Smooth and Strongly Convex Brenier Potentials in Optimal Transportcited by 19
  10. 2016Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlocited by 18
  11. 2019Estimating Convergence of Markov chains with L-Lag Couplingscited by 13
  12. 2015Leave Pima Indians alone: binary regression as a benchmark for Bayesian computationcited by 11
  13. 2020k-Variance: A Clustered Notion of Variancecited by 11
  14. 2021Bounding Wasserstein distance with couplingscited by 5
  15. 2020Coupling-based convergence assessment of some Gibbs samplers for high-dimensional Bayesian regression with shrinkage priorscited by 4

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Citing papers per year: 2024: 1; 2025: 1.

2 papers.

  1. 2024Distributional Matrix Completion via Nearest Neighbors in the Wasserstein Spacecited by 3
  2. 2025A Geometric Approach to Optimal Experimental Designcited by 2