Computational Optimal Transport for Machine Learning

COMPSCI 2840 Subject & Catalog Number

Description

Optimal Transport (OT) has quickly become an important part of the Machine Learning (ML) toolkit, where it has been used for various purposes, from learning mappings between datasets to proving convergence results for neural network training. This advanced-topics course will cover the mathematical foundations and computational aspects of OT in the context of machine learning applications. Foundational topics covered will include: Monge and Kantorovich formulations of OT, duality, entropy regularization, Gromov-Wasserstein distances, dynamic formulations, and Benamou-Brenier theory. Each of these will be presented in the context of their use for specific problems in machine learning, including domain adaptation, generative models, correspondence analysis, and gradient flows. The course combines theoretical rigor with practical exercises, implementing OT algorithms and analyzing their impact on real-world machine learning challenges. The classes will consist of a combination of instructor-led lectures on fundamentals and student-led discussion of relevant academic papers. Interested students should have a solid foundation in linear algebra, probability, and machine learning principles.