Vorlesung + Übung: Mathematische Grundlagen der KI - Details

Allgemeine Informationen

Veranstaltungsname	Vorlesung + Übung: Mathematische Grundlagen der KI
Veranstaltungsnummer	MTH-4020
Semester	SS 2025
Aktuelle Anzahl der Teilnehmenden	0
Heimat-Einrichtung	Mathematische Bildverarbeitung
Veranstaltungstyp	Vorlesung + Übung in der Kategorie Lehre
Veranstaltung findet in Präsenz statt / hat Präsenz-Bestandteile	Ja
Hauptunterrichtssprache	deutsch

Lehrende

• Prof.Dr. Stefania Petra

Räume und Zeiten

Keine Raumangabe

Studienbereiche

• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik
• Mathematisch-Naturwissenschaftlich-Technische Fakultät
• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik > Bachelor Data Science

Kommentar/Beschreibung

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.