Rémi Flamary

Emerging topics in Machine Learning

Courses

This course is done with Marylou Gabrié and is divided in two parts. I provide below the support for the first part of the course focusing on Optimal Transport for Machine Learning.

Course overview:

• Introduction to Optimal Transport [PDF]
  • Optimal transport problem
  • Wasserstein distance and geometry
  • Computational aspects and regularized OT
  • Extensions of optimal transport.
• Learning with optimal transport [PDF]
  • Mapping with Optimal Transport
  • Learning from histograms with Wasserstein distance
  • Learning from empirical distributions with Wasserstein distance
  • Learning from structured objects and across spaces

Practical session

We provide a short practical session introduction to discrete Optimal Transport. The material for te session (notebook + data) can be downloaded here.

Practical sessions will require a working Python environnement with the libraries Numpy/Scipy and Matplotlib installed. You can get such an environnement for Windows/Linux/MacOSX on Anaconda. Installing the POT Python Optimal Transport library will be necessary.

Here is a list of nice references and Python tutorials :

• Tutorial Numpy
• Doc Numpy
• Doc Scipy
• Doc ScMatplotlib/pylab

Additional references

• Marco Cuturi, Optimal transport for Machine learning, also all his publications.

• Peyré, Gabriel, and Marco Cuturi. "Computational optimal transport with applications to data science." Foundations and Trends® in Machine Learning 11.5-6 (2019): 355-607.

• OTML Workshop @ NIPS'17