Scaling Optimal Transport for High Dimensional Learning
Gabriel Peyré, CNRS and Ecole Normale Supérieure
Optimal transport (OT) has recently gained a 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.
Gabriel Peyré is a CNRS senior researcher and professor at Ecole Normale Supérieure, Paris. 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 the silver medal from CNRS in 2021. He is invited speaker at the European Congress for Mathematics in 2020. He is the deputy director of the Prairie Institute for artificial intelligence, the director of the ENS center for data science and the former director of the GdR CNRS MIA. He is the head of the ELLIS (European Lab for Learning & Intelligent Systems) Paris Unit. He is engaged in reproducible research and code education.
https://optimaltransport.github.io/, http://www.numerical-tours.com/, https://ellis-paris.github.io/