Universität Wien

250042 VU Mathematics of Machine Learning (2023S)

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. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 03.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 07.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 10.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 14.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 17.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 21.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 24.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 28.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 31.03. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 18.04. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 21.04. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 25.04. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 28.04. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 02.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 05.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 09.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 12.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 16.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 19.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 23.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 26.05. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 02.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 06.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 09.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 13.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 16.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 20.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 23.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 27.06. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 30.06. 16:45 - 18:15 Hörsaal 2 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 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

Last modified: Tu 14.03.2023 12:09