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It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds.
Integral inequalities of Poincaré and Wirtinger type for BV functions
Norman G. Meyers and William P. Ziemer · 1977
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Décomposition polaire et réarrangement monotone des champs de vecteurs
Yann Brenier · 1987
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Predicting cell lineages using autoencoders and optimal transport
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