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Moderne Signalverarbeitung für Kommunikationstechnik

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Seit WiSe 2020/21

English

Modern Signal Processing for Communications
Moderne Signalverarbeitung für Kommunikationstechnik

6

Stanczak, Slawomir

Benotet

Mündliche Prüfung

English

Zugehörigkeit


Fakultät IV

Institut für Telekommunikationssysteme

34331800 FG Netzwerk- und Informationstheorie

Keine Angabe

Kontakt


HFT 6

Reinhardt, Kerstin

sekretariat@netit.tu-berlin.de

http://www.netit.tu-berlin.de/

Lernergebnisse

The main objective of this lecture series is to give students working knowledge on a broad class of Mann-type iterative algorithms in Hilbert spaces, with focus on projection-based methods. These algorithms have been used to solve diverse problems in science and engineering such as interference reduction in MIMO systems, adaptive beamforming, peak-to-average-power-ratio (PAPR) reduction in OFDM systems, acoustic source localization, environmental modeling in wireless multi-agent systems, radio map reconstruction, and machine learning, to name a few. In the initial lectures, we start by giving students the necessary background on real Hilbert spaces and their connection to more general spaces. Students are then exposed to convex feasibility problems and vector space projection methods, and we illustrate as often as possible the mathematical concepts with concrete, real-world applications in wireless communications and signal processing. The final lectures have the objective to introduce students to fixed point algorithms based on Mann-type iterations. In the second track of lectures the students will develop a solid understanding of theoretical foundations of Machine Learning and will be able to develop, apply, and analyse the complexity of the resulting learning algorithms. A special emphasis will be put on methods for construction of efficient learning algorithms. E.g. Empirical risk minimisation via linear programming and ideas based on perceptron algorithms, stochastic subgradient methods, and support vector machines.

Lehrinhalte

The learning content includes: 1. Introduction and outline of the course 2. Metric spaces; Vector spaces; Normed vector spaces and Banach spaces; Inner products and real Hilbert spaces 3. Basics in convex analysis: convex sets, projections and relaxed projections, the fundamental theory of POCS, parallel projection methods, applications (interference reduction in communication systems, acoustic source localization with wireless sensor networks, estimation tasks in massive MIMO systems, kernel machines in sensor networks) 4. Selected topics in quasi-nonexpansive operator theory. Mann-type iterative algorithms. 5. Splitting methods for convex optimization (forward-backward splitting methods, proximal/projected gradient methods, etc.) 6. Model of learning, loss functions, and losses/risks. 7. Stochastic inequalities and concentration of measure 8. Uniform laws of large numbers, Rademacher complexity, and learning via uniform convergence. 9. Vapnik-Chervonenkis dimension and bounds on sample complexity 10. Support vector machines and kernel methods. 11. Stochastic subgradient algorithms.

Modulbestandteile

Compulsory area

Die folgenden Veranstaltungen sind für das Modul obligatorisch:

LehrveranstaltungenArtNummerTurnusSpracheSWS ISIS VVZ
Mathematical Introduction to Machine LearningVLWiSeKeine Angabe2
Modern Signal Processing for CommunicationsVL3433 L 8371SoSeen2
ISIS-Kurssuche nach Veranstaltungen des Moduls

Arbeitsaufwand und Leistungspunkte

Mathematical Introduction to Machine Learning (VL):

AufwandbeschreibungMultiplikatorStundenGesamt
Attendance15.02.0h30.0h
Pre/post processing15.04.0h60.0h
90.0h(~3 LP)

Modern Signal Processing for Communications (VL):

AufwandbeschreibungMultiplikatorStundenGesamt
Präsenzzeit15.02.0h30.0h
Vor-/Nachbereitung15.04.0h60.0h
90.0h(~3 LP)
Der Aufwand des Moduls summiert sich zu 180.0 Stunden. Damit umfasst das Modul 6 Leistungspunkte.

Beschreibung der Lehr- und Lernformen

The module consists of conventional frontal teaching in class, developing theoretical and mathematical concepts.

Voraussetzungen für die Teilnahme / Prüfung

Wünschenswerte Voraussetzungen für die Teilnahme an den Lehrveranstaltungen:

Prerequisite for participation to the module are a mathematical background at the level of beginning MS students in Electrical Engineering (Linear algebra, basic concepts of real calculus and real analysis (e.g., sequences and series of real numbers), basic knowledge of random variables). The course is open to students enrolled in any MSc in EE, CS, Mathematics and Physics.

Verpflichtende Voraussetzungen für die Modulprüfungsanmeldung:

Dieses Modul hat keine Prüfungsvoraussetzungen.

Abschluss des Moduls

Benotung

Benotet

Prüfungsform

Oral exam

Sprache(n)

English

Dauer/Umfang

60 minutes

Dauer des Moduls

Für Belegung und Abschluss des Moduls ist folgende Semesteranzahl veranschlagt:
2 Semester.

Dieses Modul kann in folgenden Semestern begonnen werden:
Winter- und Sommersemester.

Maximale teilnehmende Personen

Dieses Modul ist nicht auf eine Anzahl Studierender begrenzt.

Anmeldeformalitäten

Course teaching and organization (not module examination enrollment at Examination office/Prüfungsamt) is supported by an ISIS course. Registration details are provided at the beginning of the module in the ISIS course.

Literaturhinweise, Skripte

Skript in Papierform

Verfügbarkeit:  nicht verfügbar

 

Skript in elektronischer Form

Verfügbarkeit:  verfügbar
Zusätzliche Informationen:

 

Literatur

Empfohlene Literatur
Censor, Yair, Wei Chen, Patrick L. Combettes, Ran Davidi, and Gabor T. Herman. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints." Computational Optimization and Applications 51, no. 3 (2012): 1065-1088.
Combettes, Patrick L. "The foundations of set theoretic estimation." Proceedings of the IEEE 81, no. 2 (1993): 182-208.
I. Yamada, M. Yukawa, and M. Yamagishi, Minimizing the Moreau envelope of nonsmooth convex functions over the fixed point set of certain quasi-nonexpansive mappings, IN: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, H. Bauschke, R. Burachick, P. L.Combettes, V. Elser, D. R. Luke, and H. Wolkowicz, Eds. SpringerVerlag, 2011 (in the future, we will be also using a book currently being written by the same authors)
Luenberger, David G. Optimization by vector space methods. John Wiley & Sons, 1968.
Rudin, Walter. "Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics)." (1976) – Third Edition.
Stark, Henry, Yongi Yang, and Yongyi Yang. Vector space projections: a numerical approach to signal and image processing, neural nets, and optics. John Wiley & Sons, Inc., 1998.
Theodoridis, Sergios, Konstantinos Slavakis, and Isao Yamada. "Adaptive learning in a world of projections." Signal Processing Magazine, IEEE 28.1 (2011): 97-123.
M. Mohri, A. Rostamizadeh, A. Talwalker. “Foundations of Machine Learning”, MIT Press, 2018
R. Vershynin, “High-Dimensional Probability: An Introduction with Applications in Data Science”, Cambridge University Press, 2018
M. Wainwright, “High-Dimensional Statistics: A Non-Asymptotic Viewpoint”, Cambridge University Press, 2019
S. Shalev-Schwartz, S. Ben-David, ”Understanding Machine Learning: From Theory to Algorithms”, Cambridge University Press, 2014

Zugeordnete Studiengänge


Diese Modulversion wird in folgenden Studiengängen verwendet:

Studiengang / StuPOStuPOsVerwendungenErste VerwendungLetzte Verwendung
Computer Engineering (M. Sc.)120WiSe 2020/21SoSe 2025
Elektrotechnik (M. Sc.)120WiSe 2020/21SoSe 2025
Wirtschaftsingenieurwesen (M. Sc.)110WiSe 2020/21SoSe 2025

Studierende anderer Studiengänge können dieses Modul ohne Kapazitätsprüfung belegen.

Sonstiges

Keine Angabe