Mathematical Foundations of Machine Learning
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of WS 2020/1 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions|
|WS 2020/1||SS 2020||WS 2015/6|
MA4801 is a semester module in English language at Master’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
|Total workload||Contact hours||Credits (ECTS)|
|180 h||60 h||6 CP|
Content, Learning Outcome and Preconditions
(1) the perceptron
(2) network architecture (feedforward networks)
(3) Kolmogorov superposition theorem
(4) backpropagation and learning algorithms
(5) approximation properties of different architectures
B Kernel Methods
(1) positive definite kernels
(2) Mercer kernels
(3) reproducing kernel Hilbert spaces
(4) regularization techniques and support vector machines
(5) representer theorem for the minimizer
(6) numerical algorithms for SVM's
C Qualitative Theory
(1) loss functions
(2) risk functionals
(3) empirical risk minimization
(4) bias-variance dilemma
(6) complexity bounds
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|VO||2||Mathematical Foundations of Machine Learning||Hasenöhrl, M. Wolf, M.||
Mon, 10:15–11:45, virtuell
|UE||2||Mathematical Foundations of Machine Learning (Exercise Session)||Hasenöhrl, M. Wolf, M.||
Learning and Teaching Methods
D.J.C. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge Univ. Press 2003.
V.N. Vapnik, Statistical Learning Theory, Wiley 1998.
T. Hastie, R. Tibshirani, J. Fiedman, The Elements of Statistical Learning Theory, Springer 2009.
Description of exams and course work
The exam may be repeated at the end of the semester.