401-3619-69L  Mathematics Tools in Machine Learning

SemesterAutumn Semester 2019
LecturersF. Balabdaoui
Periodicitynon-recurring course
Language of instructionEnglish

AbstractThe course reviews many essential mathematical tools used in statistical learning. The lectures will cover the notions of hypotheses classes, sample complexity, PAC learnability, model validation and selection as well as results on several well-known algorithms and their convergence.
ObjectiveIn the exploding world of artifical intelligence and automated learning, there is an urgent need to go back to the basis of what is driving many of the well-establsihed methods in statistical learning. The students attending the lectures will get acquainted with the main theoretical results needed to establish the theory of statistical learning. We start with defining what is meant by learning a task, a training sample, the trade-off between choosing a big class of functions (hypotheses) to learn the task and the difficulty of estimating the unknown function (generating the observed sample). The course will also cover the notion of learnability and the conditions under which it is possible to learn a task. In a second part, the lectures will cover algoritmic apsects where some well-known algorithms will be described and their convergence proved.

Through the exerices classes, the students will deepen their understanding using their knowledge of the learned theory on some new situations, examples or some counterexamples.
ContentThe course will cover the following subjects:

(*) Definition of Learning and Formal Learning Models

(*) Uniform Convergence

(*) Linear Predictors

(*) The Bias-Complexity Trade-off

(*) VC-classes and the VC dimension

(*) Model Selection and Validation

(*) Convex Learning Problems

(*) Regularization and Stability

(*) Stochastic Gradient Descent

(*) Support Vector Machines

(*) Kernels
LiteratureThe course will be based on the book

"Understanding Machine Learning: From Theory to Algorithms"
by S. Shalev-Shwartz and S. Ben-David, which is available online through the ETH electronic library.

Other good sources can be also read. This includes

(*) the book "Neural Network Learning: Theoretical Foundations" de Martin Anthony and Peter L. Bartlett. This book can be borrowed from the ETH library.

(*) the lectures notes on "Mathematics of Machine Learning" taught by Philippe Rigollet available through the OpenCourseWare website of MIT
Prerequisites / NoticeBeing able to follow the lectures requires a solid background in Probability Theory and Mathematical Statistical. Notions in computations, convergence of algorithms can be helpful but are not required.