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Mathematical Foundations of Machine Learning [MA4801]

Sommersemester 2018

Prof. Dr. Michael M. Wolf

Lecturer: Prof. Dr. Michael M. Wolf
Assistant: Javier Cuesta
Lectures: Wednesday, 12:15-13:45, LMU Physik Hörsaal (Garching Forschungszentrum) Anmeldung
Exercises: Tuesday, 12:15 - 13:45, LMU Physik Hörsaal (Garching Forschungszentrum)
Friday, 14:15-15:45, room MI 02.08.020
Anmeldung

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Content

The course will provide an introduction to the mathematical foundations of supervised learning theory, neural networks, support vector machines and kernel methods.
Date Content To read Black board notes
April 11 Intro, Statistical learning theory framework, error decomposition Intro, 1.1 and 1.2 in lecture notes  
April 18 PAC bounds, growth function, VC-dimension and VC-dichotomy 1.3, 1.5 and 1.6 in lecture notes lec2
April 25 VC-dimension of vector spaces, covering and packing numbers 1.6 and 1.9 in lecture notes lec3
May 2 covering number PAC bound, pseudo and fat-shattering dimension 1.9 and 1.10 in lecture notes lec4
May 9 pseudo and fat-shattering dimension, uniform stability, on-average stability, regularization 1.10 and 1.11 in lecture notes  

Prerequisites

Basic knowledge in linear algebra, analysis and probability theory is required as well as some elementary Hilbert space theory.

Lecture notes

A preliminary version of the lecture notes can be found here (version from May 13). They will be updated on a weekly basis (hence, think twice before printing).

File Date Content Comments Solution
Exercise class 1 Week 17 - 24 April Basic probability review, Hoeffding's inequality Basic Prob. Review Solution 1
Exercise class 2 Week 24 April - 1 May PAC learning, VC dimension and VC-dichotomy Wording in H2.2 changed Solution 2
Exercise class 3 Week 8 - 15 May Covering numbers, pseudo dimension, and fat-shattering-dimension Typo in H3.3b corrected Solution 3
Exercise class 4 Week 15 - 22 May Algorithmic Stability and Uniform covering number H4.3 a bit simplified and more hints added Solution 4
Exercise class 5 Week 22 - 29 May Stability and generalized bounds    

Literature

There are many good books on the topic. Recent examples with a focus on mathematical aspects are: Among the classic books with a focus on mathematical results are: