Abstract

The field of Optimal Transport (OT) is a powerful mathematical framework that provides a natural approach for comparing probability distributions. In recent years, OT has emerged as a central topic in machine learning, largely due to the development of approximate OT solvers that can scale to large dimensions and problems. In this talk, we first briefly cover the historical and mathematical formulations of Optimal Transport theory covering the works of Monge and Kantorovich, and motivating Wasserstein distances. We then cover recent works that develop approximate, scalable OT methods such as entropic regularisation, Sinkhorn divergences and sliced Wasserstein distances. Finally, we cover recent applications of OT to the field of machine learning for classification, generative modelling, and density estimation, and briefly discuss extensions of OT to problems involving unbalanced transport (Wasserstein Fisher-Rao) and domain adaptation (Gromov Wasserstein).

Readings:

Peyré G, Cuturi M. Computational optimal transport: With applications to data science. Foundations and Trends® in Machine Learning. 2019 Feb 11;11(5-6):355-607.

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