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Mathematical Foundations of Machine Learning [MA4801]

Summer 2020

Prof. Dr. Michael Wolf

Dozent: Prof. Dr. Michael Wolf
Übungsleitung: Matthias Caro
Mitwirkende: Matthias Caro, Vjosa Blakaj, Markus Hasenöhrl
Vorlesung: Lectures and exercise classes will take place online only.

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Content

The course will provide an introduction to the mathematical foundations of learning theory and neural networks. If time allows, we will also look into kernel methods.

Date/video content
20.04 Pfeil unboxing MA4801
21.04 Pfeil probabilistic framework for supervised learning
27.04 Pfeil PAC bounds, growth function, VC-dimension
04.05 Pfeil Computing the VC-dimension
11.05 Pfeil Rademacher complexities
18.05 Pfeil Algorithmic Stability
25.05 Pfeil Sample compression
08.06 Pfeil Ensemble methods
15.06 Pfeil Neural networks & their memorization capacity
22.06 Pfeil Approximations via shallow networks
30.06 Pfeil VC-dimension of neural networks
07.07 Pfeil Deep neural networks
14.07 Pfeil Training neural networks
21.07 Pfeil Kernel methods


Lecture notes

Lecture notes will be updated once a week (usually on Tue).

Prerequisites

Basic knowledge in linear algebra, analysis and probability theory is required. For the discussion of kernel methods, we will need some elementary Hilbert space theory.

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: