Universität Wien

250042 VU Mathematics of Machine Learning (2021S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Prüfungsimmanente Lehrveranstaltung
Moodle

An/Abmeldung

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

Details

max. 30 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

The link for the zoom-meeting of the lecture will be posted on moodle before each lecture.

  • Dienstag 02.03. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 04.03. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 09.03. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 11.03. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 16.03. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 18.03. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 23.03. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 25.03. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 13.04. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 15.04. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 20.04. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 22.04. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 27.04. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 29.04. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 04.05. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 06.05. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 11.05. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 18.05. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 20.05. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 27.05. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 01.06. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 08.06. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 10.06. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 15.06. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 17.06. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 22.06. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 24.06. 11:30 - 13:00 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Dienstag 29.06. 15:00 - 16:30 Digital
    Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

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. Clustering: k-means, Lloyds algorithm, Ncut, Cheeger cut, spectral clustering.
7. Dimensionality Reduction: PCA, diffusion maps, Johnson - Lindenstrauss)
8. Neural Networks (Mostly shallow)

Art der Leistungskontrolle und erlaubte Hilfsmittel

During this lecture, there will be 3-4 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 3-4 challenges must be successfully performed to participate in the exam.

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

Mindestanforderungen und Beurteilungsmaßstab

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.

Prüfungsstoff

Everything mentioned in the lecture.

Literatur

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;

Letzte Änderung: Fr 12.05.2023 00:21