Computational Optimal Transport for Data Sciences

Optimal transport (OT) has become a fundamental mathematical tool at the interface between calculus of variations, partial differential equations and probability. It took however much more time for this notion to become mainstream in numerical applications. This situation is in large part due to the high computational cost of the underlying optimization problems. There is a recent wave of activity on the use of OT-related methods in fields as diverse as computer vision, computer graphics, statistical inference, machine learning and image processing. In this talk, I will review an emerging class of numerical approaches for the approximate resolution of OT-based optimization problems. This offers a new perspective for the application of OT in imaging sciences (to perform color transfer or shape and texture morphing) and machine learning (to perform clustering, classification and generative models in deep learning). More information and references can be found on the website of our book "Computational Optimal Transport" optimaltransport.github.io