When OT meets MoM: Robust estimation of Wasserstein Distance. (arXiv:2006.10325v3 [stat.ML] UPDATED)

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 …

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