Abstract:
Optimal transport (OT) provides rich representations of the discrepancy between probability measures supported on geometric spaces. Recently, thanks to the development of computational techniques, OT has been used to address problems involving massive datasets, as an alternative to usual KL-divergence based approaches. In this talk I will introduce the OT problem and comment on its elementary duality properties. Then, I will present the entropy regularized problem and its (fast) solution via Sinkhorn iterations. Finally, I will overview two applications to Data Science: first, dimensionality reduction via Wasserstein Barycenters and Wasserstein PCA. Second, parameter inference in generative models defined through complex nonlinear transformation of a noise distribution.
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