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 eight threehour sessions, each with a precise
topic. See tentative schedule below. Credit: 5 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 ENS (29, rue d'Ulm),
on Friday between 9am and 12pm, in the room Paul Langevin (1st floor)
The class will
follow the book in preparation (draft available here, since it will be
updated frequently, please get the latest version).
Each
student will benefit more from the class if the corresponding sections are read
before class.
Date 
Topics 
Book chapters 
October 6 
Learning with infinite data
(population setting) 
Chapter 2 

Linear Leastsquares regression 
Chapter 3 
October 20 
Empirical risk minimization 
Chapter 4 
November 3 
Optimization for machine learning 
Chapter 5 
November 10 
Local averaging techniques 
Chapter 6 
November 17 
Kernel methods 
Chapter 7 
November 24 
Model selection 
Chapter 8 
December 8 
Neural networks 
Chapter 9 
December 15 
Exam 
Evaluation
One written inclass exam.
The draft book is almost finished, and I am still looking for feedback (typos, unclear parts). Please help! (with some bonus in the final grade).