Gabriel Peyré (CNRS – Ecole Normale Supérieure) ran a Seminar@SytemX on June 17, 2020, on the following topic: « Scaling Optimal Transport for High dimensional Learning ». 


Optimal transport (OT) has recently gained lot of interest in machine learning. It is a natural tool to compare in a geometrically faithful way probability distributions. It finds applications in both supervised learning (using geometric loss functions) and unsupervised learning (to perform generative model fitting). OT is however plagued by the curse of dimensionality, since it might require a number of samples which grows exponentially with the dimension. In this talk, I will review entropic regularization methods which define geometric loss functions approximating OT with a better sample complexity. More information and references can be found on the website of our book “Computational Optimal Transport”.


Gabriel Peyré is CNRS research director in the mathematics and applications department of the École Normale Supérieure and Professor at the ENS. He works at the interface between applied mathematics, imaging and machine learning. He obtained 2 ERC grants (starting in 2010 and consolidator in 2017), the Blaise Pascal prize from the French Academy of Sciences in 2017, the Magenes Prize from the Italian Mathematical Union in 2019 and is invited speaker at the European Congress for Mathematics in 2020. He is the deputy director of the 3IA Prairie Institute as well as the director of the ENS center for data sciences, and former director of the GdR CNRS MIA.

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