# When OT meets MoM: Robust estimation of Wasserstein Distance

arXiv: https://arxiv.org/abs/2006.10325 · HTML: https://mlsanity.com/paper/2006.10325/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2020.

## Built on by (most cited first, 23 of 23)

- [Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances](https://mlsanity.com/paper/2210.09160/) (2022)
- [Automatic Text Evaluation through the Lens of Wasserstein Barycenters](https://mlsanity.com/paper/2108.12463/) (2021)
- [InfoLM: A New Metric to Evaluate Summarization & Data2Text Generation](https://mlsanity.com/paper/2112.01589/) (2021)
- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regions](https://mlsanity.com/paper/2103.12711/) (2021)
- [Learning Disentangled Textual Representations via Statistical Measures of Similarity](https://mlsanity.com/paper/2205.03589/) (2022)
- [Optimal Transport for Unsupervised Hallucination Detection in Neural Machine Translation](https://mlsanity.com/paper/2212.09631/) (2022)
- [Uniform Concentration Bounds toward a Unified Framework for Robust Clustering](https://mlsanity.com/paper/2110.14148/) (2021)
- [Robust Estimation under the Wasserstein Distance](https://mlsanity.com/paper/2302.01237/) (2023)
- [Regroup Median Loss for Combating Label Noise](https://mlsanity.com/paper/2312.06273/) (2023)
- [Fast Topological Clustering with Wasserstein Distance](https://mlsanity.com/paper/2112.00101/) (2021)
- [Robust Principal Component Analysis: A Median of Means Approach](https://mlsanity.com/paper/2102.03403/) (2021)
- [Hypothesis Transfer Learning with Surrogate Classification Losses: Generalization Bounds through Algorithmic Stability](https://mlsanity.com/paper/2305.19694/) (2023)
- [Sharp error bounds for imbalanced classification: how many examples in the minority class?](https://mlsanity.com/paper/2310.14826/) (2023)
- [MAPPING: Debiasing Graph Neural Networks for Fair Node Classification with Limited Sensitive Information Leakage](https://mlsanity.com/paper/2401.12824/) (2024)
- [A Novel Information-Theoretic Objective to Disentangle Representations for Fair Classification](https://mlsanity.com/paper/2310.13990/) (2023)
- [Signature Isolation Forest](https://mlsanity.com/paper/2403.04405/) (2024)
- [Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification](https://mlsanity.com/paper/2201.01973/) (2022)
- [Learning Weighting Map for Bit-Depth Expansion within a Rational Range](https://mlsanity.com/paper/2204.12039/) (2022)
- [On making optimal transport robust to all outliers](https://mlsanity.com/paper/2206.11988/) (2022)
- [Robust computation of optimal transport by β-potential regularization](https://mlsanity.com/paper/2212.13251/) (2022)
- [Distribution Estimation of Contaminated Data via DNN-based MoM-GANs](https://mlsanity.com/paper/2212.13741/) (2022)

## 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.