Universität Wien

250095 VU Mathematics of Machine Learning (2025S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Prüfungsimmanente Lehrveranstaltung
GEMISCHT
Moodle
Di 29.04. 13:15-14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 25 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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.

  • Dienstag 04.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 06.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 11.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 13.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 18.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 20.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 25.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 27.03. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 01.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 03.04. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 08.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 10.04. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 06.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 08.05. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 13.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 15.05. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 20.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 22.05. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 27.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 03.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 05.06. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 10.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 12.06. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Dienstag 17.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 24.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 26.06. 09:45 - 11:15 Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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.

Mindestanforderungen und Beurteilungsmaßstab

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.

Prüfungsstoff

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

Literatur

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/

Zuordnung im Vorlesungsverzeichnis

MAMV;MSTV;MANV

Letzte Änderung: Di 25.02.2025 08:46