BIGOT, Jérémie; CAZELLES, Elsa; PAPADAKIS, Nicolas

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BIGOT, Jérémie
Institut de Mathématiques de Bordeaux [IMB]

CAZELLES, Elsa
Institut de Mathématiques de Bordeaux [IMB]

PAPADAKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

Electronic Journal of Statistics. 2019, vol. 13, n° 2, p. 5120-5150

Shaker Heights, OH : Institute of Mathematical Statistics

Résumé en anglais

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data analysis. The Sinkhorn divergence allows the fast computation of an entropically regularized Wasserstein distance between two probability distributions supported on a finite metric space of (possibly) high-dimension. For data sampled from one or two unknown probability distributions, we derive the distributional limits of the empirical Sinkhorn divergence and its centered version (Sinkhorn loss). We also propose a bootstrap procedure which allows to obtain new test statistics for measuring the discrepancies between multivariate probability distributions. Our work is inspired by the results of Sommerfeld and Munk (2016) on the asymptotic distribution of empirical Wasserstein distance on finite space using unregularized transportation costs. Incidentally we also analyze the asymptotic distribution of entropy-regularized Wasserstein distances when the regularization parameter tends to zero. Simulated and real datasets are used to illustrate our approach.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192955

Project ANR

Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010

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Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251