Introduction

In recent years, machine learning research has been an avid consumer of advanced methods in stochastic calculus and stochastic analysis. The aim of this course is to lay out the foundations and explore recent applications of these tools. Among the topics we intend to cover are: (1) Reversed diffusion processes and generative AI algorithms (2) Stochastic control and neural networks (3) Rough paths and the signature method for machine learning (4) Relaxed control and reinforcement learning We will first review the mathematical background required to fully grasp each of those themes.

This is a vertical space

Bibliography

1. I. Karatzas and S.E. Shreve, Brownian motion and stochastic calculus, second edition, Graduate Texts in Mathematics, 113, Springer, New York, 1991.
2. J. Yong and X.Y. Zhou, Stochastic controls, Applications of Mathematics 43, Springer, New York, 1999.
3. X. Geng, An Introduction to the Theory of Rough Paths, Link.

This is a vertical space

Calendar

Here is a link to an approximate calendar, subject to changes.

This is a vertical space

Projects

Here is a link to our reading projects list, still to be updated.

Rules for the projects:

1. Choose a proper topic.
   Select a reasonable bibliography. The theoretical content has to be substantial.
2. Write a 10 pages report on your topic. Mathematical steps must be rigorous and well explained.
3. Coding some of the methods is allowed, but should not be thought of as a substitute for math contents.
4. There will be a 30mn presentation with slides for each group. No more than 20 slides should be used for this presentation.
5. Slides for the presentations should not be too dense.

This is a vertical space

Slides (Feedback on typos appreciated)

This is a vertical space

Notes in book form (Feedback also appreciated)

This is a vertical space

Documents with computations (notes from lectures)

This is a vertical space

Back to Maths Department homepage