Modulbeschreibung MA5442

# Modulbeschreibung

## MA5442: High-dimensional Statistics

### Fakultät für Mathematik

Modulniveau:
Master
Sprache:
Englisch
Semesterdauer:
Einsemestrig
Häufigkeit:
Unregelmäßig
Credits*:
5
Gesamt-
stunden:

150
Eigenstudiums-
stunden:

105
Präsenz-
stunden:

45
* Die Zahl der Credits kann in Einzelfällen studiengangsspezifisch variieren. Es gilt der im Transcript of Records oder Leistungsnachweis ausgewiesene Wert.
Beschreibung der Studien-/Prüfungsleistungen:
The module examination is based on a written exam with video surveillance (90 minutes). The exam tests that students have gained a deeper understanding of statistical methods for analysis of high-dimensional data and are able to apply the methods to specific examples. The students are expected to be able to derive the methods and to explain their mathematical properties and limitations.
Wiederholungsmöglichkeit:
Im Folgesemester: Nein
Am Semesterende: Ja
(Empfohlene) Voraussetzungen:
MA1401 Einführung in die Wahrscheinlichkeitstheorie/MA2409 Wahrscheinlichkeitstheorie, MA2402 Statistik Grundlagen, MA3403 Generalized Linear Models
Angestrebte Lernergebnisse:
Upon successful completion of this module, students understand the challenges arising in statistical analysis of high-dimensional data and are able to devise appropriate methods to address these challenges. In particular, they are able to apply corrections to control false discoveries in large-scale multiple testing problems. Furthermore, they are able to devise methods that exploit low-dimensional structure in regression problems. Moreover, the students know how to tackle high-dimensional problems in multivariate statistics using regularization methods for graphical models and for estimation of matrix-valued parameters.
Inhalt:
This course covers:
- multiple testing and methods for control of the false discovery rate,
- linear models and the lasso estimator for sparse high-dimensional regression,
- group-sparsity and other forms of low-dimensional signals,
- extensions to generalized linear models,
- methods for estimation of matrix-valued parameters,
- high-dimensional graphical models.

The lectures will give brief reviews of the involved statistical concepts and then introduce methods suitable for high-dimensional data. The lectures will develop theoretical properties of the methods and discuss involved optimization issues.
Lehr- und Lernmethode:
This module is offered as a lecture course with an exercise class. The lectures serve to introduce and exemplify new concepts and methods, and to develop theoretical results. The exercise class and exercise sheets will deepen the students' understanding of the covered methodology and its theoretical properties, and take the students through detailed examples.
Medienformen:
blackboard, slides, moodle
Literatur:
Giraud, Christophe. Introduction to high-dimensional statistics. Monographs on Statistics and Applied Probability, 139. CRC Press, Boca Raton, FL, 2015.
Hastie, Trevor; Tibshirani, Robert; Wainwright, Martin. Statistical learning with sparsity. The lasso and generalizations. Monographs on Statistics and Applied Probability, 143. CRC Press, Boca Raton, FL, 2015.
Wainwright, Martin. High-dimensional statistics. A non-asymptotic viewpoint. Cambridge Series in Statistical and Probabilistic Mathematics, 48. Cambridge University Press, Cambridge, 2019.
Bühlmann, Peter; van de Geer, Sara. Statistics for high-dimensional data. Methods, theory and applications. Springer Series in Statistics. Springer, Heidelberg, 2011.
Modulverantwortliche(r):
Drton, Mathias; Prof. Dr.: mathias.drton@tum.de
Lehrveranstaltungen (Lehrform, SWS) Dozent(in):

0000005647 High-dimensional Statistics [MA5442] (2SWS VO, WS 2020/21)
Drton M

0000005882 Exercises for High-dimensional Statistics [MA5442] (1SWS UE, WS 2020/21)
Drton M, Dettling P