The
class will be taught in French or (most probably) English, depending on
attendance (all slides and class notes are in English).
Summary
The goal of this class is to present
old and recent results in learning theory, for the most widelyused learning
architectures. This class is geared towards theoryoriented students as well as
students who want to acquire a basic mathematical understanding of algorithms
used throughout the masters
program.
A particular effort will be made to
prove many results from first principles, while keeping the exposition as
simple as possible. This will naturally lead to a choice of key results that
showcase in simple but relevant instances the important concepts in learning
theory. Some general results will also be presented without proofs.
The class will be organized in nine
threehour sessions, each with a precise topic (a chapter from the book in
preparation "Learning theory from first principles"). See tentative
schedule below. Credit: 4 ECTS.
Prerequisites: We will prove results
in class so a good knowledge of undergraduate mathematics is important, as well
as basic notions in probability. Having followed an introductory class on
machine learning is beneficial.
Dates
All
classes will be "in real life" at the auditorium of Parisanté Campus, on Thursdays between 9am and 12.15pm.
The class
will follow the book (final draft available here)
Each
student will benefit more from the class if the corresponding sections are read
before class.
Date 
Topics 
Book chapters 
September 19 
Learning with infinite data
(population setting) 
Chapter 2 

Linear Leastsquares regression 
Chapter 3 
October 10 
Empirical risk minimization 
Chapter 4 
October 17 
Optimization for machine learning 
Chapter 5 
November 7 
Local averaging techniques 
Chapter 6 
November 14 
Kernel methods 
Chapter 7 
November 21 
Model selection 
Chapter 8 
December 5 
Neural networks 
Chapter 9 
December 12 
Overparameterized models 
Chapter 12 
December 18 
Exam 
Evaluation
Takehome exercises (25%). One written inclass exam (75%).
Extra points for writing in latex solutions to exercises from the textbook.