← Zurück zur Übersicht
14114Fakultät 1 – MINT – Mathematik, Informatik, Physik, Elektro- und Informationstechnik
Hochdimensionale Statistiken
Titel auf Englisch: High-Dimensional Statistics
Lernergebnisse
After successfully completing the module, students have deepened their knowledge of stochastics acquired in the basic modules. They know the mathematical and statistical methods from data analysis. They have acquired basic skills for in-depth modules in stochastics or optimization. They also have experience in doing independent research.
Inhalte
- Concentration of random vectors in high dimensions
- Concentration inequalities
- Linear and nonlinear principal component analysis (PCA)
- Random matrices
- Sparse recovery (compressed sensing) and LASSO regression
- Introduction to statistical learning
- Kernel methods and Gaussian processes
- Applications in signal and image processing, random networks, …
Voraussetzungen
Verpflichtende Voraussetzungen
Keine
Empfohlene Voraussetzungen
- 11103: Analysis I
- 11104: Analysis II
- 11101: Lineare Algebra und analytische Geometrie I
- 11217: Wahrscheinlichkeitstheorie
- 11113: Mathematics IT-2 (Linear Algebra)
- 11213: Mathematics IT-3 (Analysis)
- as well as of the content one of the modules - 11917: Mathematik W-3 (Statistik) - 11926: Statistik für Anwender - 11212: Statistics
Prüfungsmodalitäten
- Successful completion of a semester project
- Project presentation, 45 min.
Angeboten in
- Artificial IntelligenceM.Sc.
Wahlpflichtkomplex: Learning and Reasoning
- InformatikB.Sc.
Wahlpflichtkomplex: Applied Mathematics
- InformatikB.Sc.
Wahlpflichtkomplex: Mathematics
| Studiengang | Abschluss | Wahlpflichtkomplex |
|---|---|---|
| Artificial Intelligence | M.Sc. | Learning and Reasoning |
| Informatik | B.Sc. | Applied Mathematics |
| Informatik | B.Sc. | Mathematics |
Literatur und Materialien
- C.M. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.
- D.P. Dubhashi, A. Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms, Cambridge University Press, 2009.
- R. van Handel. Probability in High Dimension. Lecture Notes, Princeton University, 2016.
- R. Vershynin. High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge University Press, 2018
Bewertungen von Studierenden
Was Studierende über dieses Modul sagen. Die BTU hat damit nichts zu tun — hier schreiben nur Studierende, und jede Bewertung ist die Meinung einer einzelnen Person.