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Lecturer: Marc SEBBAN, Pr., Laboratoire Hubert Curien (UJM, CNRS, IOGS) - Saint-Étienne Abstract: Optimal Transport has become a popular tool during the past few years in the machine learning community for aligning statistical distributions. Given transportation costs between two sets of samples that have been respectively drawn from a source and a target distribution, the goal in the discrete case is to learn a transport plan that minimizes the global alignment cost between the two sets. The resulting measure is called the Wasserstein distance and defines a distance in the space of probability measures. In this lecture, we will introduce the main concepts of the theory of Optimal Transport and show that the Wasserstein distance can be of great interest to address many machine learning and computer vision problems ranging from applications in domain adaptation, image processing, natural language processing, deep learning, to cite a few.