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Mathematical Foundations of Machine Learning [MA4801]

Sommersemester 2016

Prof. Dr. Michael M. Wolf

Dozent: Prof. Dr. Michael M. Wolf
Übungsleitung:  
Mitwirkende:  
Vorlesung: Tuesday, 14:15-16:00, MI HS3 Anmeldung
Übung: Wednesday, 10:00-11:30, room 00.08.059
Thursday, 14:00-16:00, room 02.13.010
Friday, 12:00-14:00, room 03.06.011
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Content

The course will provide an introduction into the mathematical foundations of learning theory, neural networks, support vector machines and kernel methods.

Prerequisites

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

Notes

Preliminary lecture notes (ideally updated weekly, after every lecture) can be found here (last update: Nov 17th). This also contains some of the solutions to the exercises.

File Date Content Comments Solution
Exercise class 1 Week 13 - 20 April ERM, error decomposition, Hoeffding's inequality   Solution 1
Exercise class 2 Week 21 - 29 April PAC learning   Solution 2
Exercise class 3 Week 9-13 May Growth function and VC-dimension   Solution 3
Exercise class 4 Week 16-20 May Concentration inequalities and Rademacher complexities   Solution 4
Exercise class 5 Week 1-3 June Adaboost, Neural Networks   see lecture notes
Exercise class 6 Week 8-10 June VCdim and Rademacher complexities of neural networks    
Exercise class 7 Week 15-17 June Neural networks - complexity and geometry   see lecture notes
Exercise class 8 Week 22-24 June Recap    
Exercise class 9 Week 29-30 June Rademacher complexity with margin, KKT and support vectors    
Exercise class 10 1st week of July Kernels   Solution 10
Exercise class 11 2nd week of July Open discussion / preparation for the exam   Problems with solutions 11

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: