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François-Pierre PATY (CREST) – "An Introduction to Optimal Transport"

November 20, 2019 @ 2:00 pm - 3:00 pm | Organizers: Nicolas Schreuder, François-Pierre Paty, Nicolas Schreuder
The Statistics-Econometrics-Machine Learning Seminar.
Time: 14:00 pm – 15:00 pm
Date: 20th of November 2019
Place: Room 3001.
François-Pierre PATY (CREST) – “An Introduction to Optimal Transport”
 Abstract : Optimal transport (OT) dates back to the end of the 18th century, when French mathematician Gaspard Monge proposed to solve the problem of déblais and remblais. Yet, the mathematical formulation of Monge was rapidly found to meet its limits in the lack of provable existence of the studied objects. It is only after 150 years that OT enjoyed a resurgence, when Kantorovich understood the suitable framework that would allow to solve Monge’s problem and give rise to fundamental tools and theories in probability, optimization, differential equations and geometry. While applications in economics have a long history, it has only been recently that OT has been applied to statistics and machine learning, as a way to analyze data. In this mini-lecture, I will first define OT and present the most prominent results of OT theory. Then, I will give an overview of the current research in statistical and algorithmic OT, with an emphasis on machine learning and economics applications.