Optimal Transport Meets Machine Learning

Slides

• Gabriel Peyré (CNRS and ENS): an introduction to Optimal Transport.
• Marco Cuturi, (ENSAE): numerical methods for Optimal Transport.
• Nicolas Courty, (IRISA): Optimal Transport for Machine Learning

Computational resources

• Sinkhorn solver by Marco Cuturi.
• The numerical Tours of Signal Processing (in Matlab and Python) contains a section dedicated to the basics of computational optimal transport (linear solver, entropic regularization, applications to imaging sciences).
• Python Optimal Transport Library: This open source Python library provide several solvers for optimization problems related to Optimal Transport for signal, image processing and machine learning.
• Unbalanced Transport in Matlab, in Julia, and python (including space and multiscale): codes to solve entropic OT, barycenters, gradient flows, with mass variation.

Bibliography

Here is a (biased) bibliography related to the lectures:

• F. Santambrogio, Optimal Transport for Applied Mathematicians, review the basics of the mathematics underlying OT.
• M. Cuturi, Sinkhorn Distances: Lightspeed Computation of Optimal Transport, NIPS 2013.
• J-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, G. Peyré. Iterative Bregman Projections for Regularized Transportation Problems. SIAM Journal on Scientific Computing, 37(2), pp. A1111–A1138, 2015.
• N. Courty, R. Flamary, D. Tuia, A. Rakotomamonjy, Optimal Transport for Domain Adaptation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016
• R. Flamary, C. Févotte, N. Courty, V. Emiya, Optimal spectral transportation with application to music transcription, NIPS, 2016.