Universität Wien

250095 VU Mathematics of Machine Learning (2025S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
MIXED
Moodle
Tu 17.06. 13:15-14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

The Tuesday lecture will usually be online, because I often will need to present coding examples, which I can do much better from my computer at home.

  • Tuesday 04.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 06.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 11.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 18.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 25.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 01.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.04. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 08.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.04. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 29.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 06.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 08.05. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 13.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.05. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 20.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.05. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 27.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.06. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 10.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.06. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 24.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.06. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

We will introduce the basic concepts of the mathematics behind machine learning. This lecture deals with classical machine learning as compared to deep learning, which is the topic of another lecture.
Topics include:
1. PAC Theory: PAC Learning model, finite hypothesis sets, consistent and inconsistent problems, deterministic and agnostic learning,
2. Rademacher complexity and VC dimension: generalization bounds for Rademacher, Growth function, Connection to Rademacher compl., VC dimension, VC dimension based upper bounds,
lower bounds on generalization.
3. Model Selection: Bias Variance trade-off, Structural Risk minimisation, Cross validation, regularisation
4. Support Vector Machines: generalisation bounds, margin theory/margin based generalization bounds
5. Kernel Methods: Reproducing Kernel Hilbert spaces, Representer Theorem, kernel SVM, generalisation bounds for kernel based methods
6. Boosting and Ensemble Methods,
7. Clustering: k-means, Lloyds algorithm, Ncut, Cheeger cut, spectral clustering.
8. Dimensionality Reduction: PCA, diffusion maps, Johnson - Lindenstrauss)
9. Neural Networks (Mostly shallow)

This is an applied math course. Therefore it will often touch on many different mathematical fields. Such as harmonic analysis, graph theory, random matrix theory, etc. students are not required to know about these issues beforehand. But a certain willingness to look up concepts from time to time is necessary.

Assessment and permitted materials

During this lecture, there will be at least three challenges. In which you will have to solve machine learning problems. You can use any programming language you like, but Python is advised.
In these challenges, you need to beat the base-line of an algorithm that I propose. All three challenges must be completed successfully to participate in the exam.

There will be an oral exam at the end of the lecture.

Minimum requirements and assessment criteria

Successful participation in all challenges and a basic understanding of all concepts introduced in the lecture is required for passing.

To achieve the best grade, all concepts and results need to be understood in depth this includes the ability to prove all results.

Examination topics

Everything covered in the lecture. This is documented in the lecture notes.

Reading list

Lecture notes will be made available in moodle.

The lecture is based on the following books:

1. Mohri, Mehryar, Afshin Rostamizadeh, and Ameet Talwalkar. Foundations of machine learning. MIT press, 2018. \url{https://cs.nyu.edu/~mohri/mlbook/

2. Shalev-Shwartz, Shai, and Shai Ben-David. Understanding machine learning: From theory to algorithms. Cambridge university press, 2014. https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/

3. Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. The elements of statistical learning: data mining, inference, and prediction. Springer Science \& Business Media, 2009 https://web.stanford.edu/~hastie/ElemStatLearn/

Association in the course directory

MAMV;MSTV;MANV

Last modified: Tu 25.02.2025 08:46