Intensive course on numerical optimal transport

There will be a 3-day intensive course on numerical aspects of optimal transport, given by Gabriel Peyré, which will take place at the IMT on March 20-22. Additionally, two introductory lectures on optimal transport will take place on March 18th and 19th.

Description: 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 short course, I will review numerical approaches for the approximate resolution of optimization problems related to optimal transport. I will also give some insight on how to apply these methods to imaging sciences and machine learning problems. The course will feature a numerical session using Python. Material for the course (including a small book, slides and computational resources) can be found online at https://optimaltransport.github.io/.

Schedule:
Course 1: Foundations of Optimal Transport
   - Overview of applications in imaging and learning
   - Simplex algorithm
   - Network flows solvers
   - Semi-discrete, auction
Course 2: Entropic regularization
   - Regularization and approximation
   - Sinkhorn's algorithm
   - Hilbert's metric, Perron-Frobenius
   - Extensions: multimarginal, barycenters, unbalanced
Course 3: Statistical Estimation and Learning
   - Statistical divergences
   - Sample complexity
   - Minimum Kantorovich Estimator
   - Deep learning and generative models

Schedule:
-Monday 18/03 and Tuesday 19/03 from 1:30pm until 3:30pm, salle MIP, 1R2 (introductory lectures)
-Wednesday 20/03 and Thursday 21/03 from 1:30pm until 3:30pm, Amphi Schwartz, 1R2
-Friday 22/03 from 10am to 12am, , Amphi Schwartz, 1R2

There will also be a numerical session on Thursday from 4pm to 5:30pm.