Theoretical Foundations of Machine Learning

The course covers the key algorithmic principles in machine learning as well as their theoretical foundation and analysis. The learning problem is introduced in the framework of statistical learning theory. The course then focuses on linear and nonlinear models (kernel methods and neural networks) learned through empirical risk minimization and regularization. The key tools to study these models from a functional analytic perspective will be introduced, including the theory of reproducing kernel Hilbert spaces. Computational aspects will be covered, introducing key ideas in convex analysis and optimization, including gradient and stochastic gradient methods, splitting methods, and back-propagation. Finally, statistical and approximation properties will be analyzed using concentration of measure and empirical process theory, along with spectral calculus and operator theory. Two tutorials by invited speakers are planned for Wednesday morning.

The course spans five days, with lectures held in the mornings and afternoons, except on Wednesday, which includes only morning tutorials. Attendance is required and will be registered before each session. Students will have the chance to take a final exam (modalities TBC). Students will receive an attendance certificate indicating the number of hours they attended, provided that it is no less than 80% of the total course hours.
The school will take place exclusively in person, it will not be streamed online nor recorded. Please note that there is no scholarship available to cover travel and accommodation costs.

The course is advanced and covers theoretical aspects, hence it is targeted to students with solid mathematical background, particularly in probability theory, advanced calculus and linear algebra.