Optimal Transport for Machine Learning

This lecture covers the concept of optimal transport for machine learning, focusing on comparing distributions, unsupervised learning, Monge's problem, Kantorovitch's formulation, optimal transport distances, entropic regularization, Sinkhorn's algorithm, the curse and blessings of optimal transport, unbalanced optimal transport, Gromov-Wasserstein metric, shape registration, and open problems in high-dimensional optimal transport. The instructor discusses the challenges and applications of optimal transport in various fields, such as single-cell multi-omics and developmental trajectories inference.