Universität Wien

250042 VU Mathematics of Machine Learning (2021S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
Moodle

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. 30 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

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

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

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

Assessment and permitted materials

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.

Minimum requirements and assessment criteria

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.

Examination topics

Everything mentioned in the lecture.

Reading list

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;

Last modified: Fr 12.05.2023 00:21