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Tutorial
A Primer on Optimal Transport
Marco Cuturi · Justin M Solomon

Mon Dec 04 08:00 AM -- 10:15 AM (PST) @ Grand Ballroom

Optimal transport (OT) provides a powerful and flexible way to compare probability measures, discrete and continuous, which includes therefore point clouds, histograms, datasets, parametric and generative models. Originally proposed in the eighteenth century, this theory later led to Nobel Prizes for Koopmans and Kantorovich as well as Villani’s Fields Medal in 2010. OT recently has reached the machine learning community, because it can tackle challenging learning scenarios including dimensionality reduction, structured prediction problems that involve histogram outputs, and estimation of generative models such as GANs in highly degenerate, high-dimensional problems. Despite very recent successes bringing OT from theory to practice, OT remains challenging for the machine learning community because of its mathematical formality. This tutorial will introduce in an approachable way crucial theoretical, computational, algorithmic and practical aspects of OT needed for machine learning applications.

Author Information

Marco Cuturi (Google Brain & CREST - ENSAE)

Marco Cuturi is a research scientist at Google AI, Brain team in Paris. He received his Ph.D. in 11/2005 from the Ecole des Mines de Paris in applied mathematics. Before that he graduated from National School of Statistics (ENSAE) with a master degree (MVA) from ENS Cachan. He worked as a post-doctoral researcher at the Institute of Statistical Mathematics, Tokyo, between 11/2005 and 3/2007 and then in the financial industry between 4/2007 and 9/2008. After working at the ORFE department of Princeton University as a lecturer between 2/2009 and 8/2010, he was at the Graduate School of Informatics of Kyoto University between 9/2010 and 9/2016 as a tenured associate professor. He joined ENSAE in 9/2016 as a professor, where he is now working part-time. His main employment is now with Google AI (Brain team in Paris) since 10/2018, as a research scientist working on fundamental aspects of machine learning.

Justin M Solomon (MIT)

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