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Regularized Optimal Transport and Applications

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Optimal transport theory provides tools to compare probability measures. After reviewing the basics of optimal transport distances (a.k.a Wasserstein or Earth Mover’s), I will show how an adequate regularization of the optimal problem can result in substantially faster computations and much better behaved numerical computations. I will then show how this regularization can enable several applications of optimal transport to learn from probability measures, from the computation of barycenters to that of dictionaries or PCA , all carried out using the Wasserstein geometry.

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