Optimal Transport for PDEs and Machine Learning
Jussieu -- salle 15-16-309 4 Place Jussieu, Paris, FranceOptimal transport (OT) has recently gained significant interest in statistics and machine learning. It serves as a natural tool for comparing probability distributions in a geometrically faithful manner. However, OT faces challenges due to the curse of dimensionality, as it may require a sample size that grows exponentially with the dimension. This seminar will be divided into two parts: A tutorial on optimal transport, where I will review the Monge and Kantorovich formulations, and their connection to gradient flow PDEs via the minimizing movement scheme. A more advanced discussion on […]