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Vorlesung + Übung: Mathematische Grundlagen der KI - Details
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General information

Course name Vorlesung + Übung: Mathematische Grundlagen der KI
Subtitle Mathematics of Machine Learning: An Introduction
Course number MTH-4020
Semester SS 2024
Current number of participants 25
Home institute Institut für Mathematik
Courses type Vorlesung + Übung in category Teaching
Preliminary discussion Tuesday, 16.04.2024 15:45 - 17:15
First date Tuesday, 16.04.2024 15:45 - 17:15, Room: (1008 L)
Online/Digitale Veranstaltung Veranstaltung wird in Präsenz abgehalten.
Hauptunterrichtssprache deutsch

Rooms and times

(1008 L)
Tuesday, 16.04.2024, Tuesday, 23.04.2024 - Wednesday, 24.04.2024, Tuesday, 30.04.2024, Tuesday, 07.05.2024 - Wednesday, 08.05.2024, Tuesday, 14.05.2024 - Wednesday, 15.05.2024 15:45 - 17:15

Module assignments

Comment/Description

Mathematical Foundation of AI (Vorlesung + Übung)

This course offers a comprehensive journey through essential mathematical foundations and practical techniques in machine learning and data analysis. Starting from basic mathematical concepts like matrix factorizations and parametric probability distributions, to exploring more advanced topics such as reproducing kernel Hilbert spaces and numerical optimization, students will develop a robust understanding for tackling real-world data challenges. Through hands-on exercises and computational projects, participants will gain proficiency in data embeddings, unsupervised learning, clustering, supervised learning for classification and regression, as well as density estimation. Additionally, the course introduces students to the exciting realm of deep learning, providing a solid foundation for further exploration in this rapidly evolving field.

Content:
- Math. background (matrix factorizations, RKHS, convex optimization: unconstrained, QPs)
- Data embeddings: MDS, spectral embeddings, RKHS embeddings
- Data exploration: clustering (pairwise vs.~prototypes)
- Dimension reduction and visualization: PCA, KPCA, t-SNE
- Supervised learning, classification: kNN, SVM
- Classification: statistical performance, bias-variance tradeoff, generalization
- Supervised learning, regression: kernel-ridge regression, Ausblick: GP
- Supervised learning, density estimation: parametric, nonparametric
- Deep learning: Introduction

Literature:
J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis, Cambridge University Press, 2004
S. Shalev-Shwartz and S. Ben-David. Understanding Machine Learning. Cambridge Univ. Press, 2014.
M. Hardt and B. Recht. Patterns, Predictions, and Actions: Foundations of Machine Learning. Princeton University Press, 2022.
P. Grohs and G. Kutyniok, editors. Mathematical Aspects of Deep Learning. Cambridge University Press, 2022.