mlsanityData to 7 Oct 2026

When OT meets MoM: Robust estimation of Wasserstein Distance

arXiv 2006.10325 ↗First posted 18 Jun 2020stat.ML cs.LGcited by 23

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Abstract (arXiv)

Issued from Optimal Transport, the Wasserstein distance has gained importance in Machine Learning due to its appealing geometrical properties and the increasing availability of efficient approximations. In this work, we consider the problem of estimating the Wasserstein distance between two probability distributions when observations are polluted by outliers. To that end, we investigate how to leverage Medians of Means (MoM) estimators to robustify the estimation of Wasserstein distance. Exploiting the dual Kantorovitch formulation of Wasserstein distance, we introduce and discuss novel MoM-based robust estimators whose consistency is studied under a data contamination model and for which convergence rates are provided. These MoM estimators enable to make Wasserstein Generative Adversarial Network (WGAN) robust to outliers, as witnessed by an empirical study on two benchmarks CIFAR10 and Fashion MNIST. Eventually, we discuss how to combine MoM with the entropy-regularized approximation of the Wasserstein distance and propose a simple MoM-based re-weighting scheme that could be used in conjunction with the Sinkhorn algorithm.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2020.

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Citing papers per year: 2021: 7; 2022: 9; 2023: 5; 2024: 2.

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  1. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  2. 2021Automatic Text Evaluation through the Lens of Wasserstein Barycenterscited by 38
  3. 2021InfoLM: A New Metric to Evaluate Summarization & Data2Text Generationcited by 33
  4. 2021Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysiscited by 27
  5. 2022RipsNet: a general architecture for fast and robust estimation of the persistent homology of point cloudscited by 20
  6. 2021A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regionscited by 17
  7. 2022Learning Disentangled Textual Representations via Statistical Measures of Similaritycited by 14
  8. 2022Optimal Transport for Unsupervised Hallucination Detection in Neural Machine Translationcited by 13
  9. 2021Uniform Concentration Bounds toward a Unified Framework for Robust Clusteringcited by 10
  10. 2023Robust Estimation under the Wasserstein Distancecited by 8
  11. 2023Regroup Median Loss for Combating Label Noisecited by 8
  12. 2021Fast Topological Clustering with Wasserstein Distancecited by 5
11 more
  1. 2021Robust Principal Component Analysis: A Median of Means Approachcited by 4
  2. 2023Hypothesis Transfer Learning with Surrogate Classification Losses: Generalization Bounds through Algorithmic Stabilitycited by 4
  3. 2023Sharp error bounds for imbalanced classification: how many examples in the minority class?cited by 4
  4. 2024MAPPING: Debiasing Graph Neural Networks for Fair Node Classification with Limited Sensitive Information Leakagecited by 2
  5. 2023A Novel Information-Theoretic Objective to Disentangle Representations for Fair Classificationcited by 1
  6. 2024Signature Isolation Forestcited by 1
  7. 2022Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecificationcited by 0
  8. 2022Learning Weighting Map for Bit-Depth Expansion within a Rational Rangecited by 0
  9. 2022On making optimal transport robust to all outlierscited by 0
  10. 2022Robust computation of optimal transport by β-potential regularizationcited by 0
  11. 2022Distribution Estimation of Contaminated Data via DNN-based MoM-GANscited by 0