Helmut Bölcskei: Katalogdaten im Frühjahrssemester 2020

NameHerr Prof. Dr. Helmut Bölcskei
LehrgebietMathematische Informationswissenschaften
Adresse
Professur Math. Informationswiss.
ETH Zürich, ETF E 122
Sternwartstrasse 7
8092 Zürich
SWITZERLAND
Auszeichnung: Die Goldene Eule
Telefon+41 44 632 34 33
E-Mailhboelcskei@ethz.ch
URLhttps://www.mins.ee.ethz.ch/people/show/boelcskei
DepartementInformationstechnologie und Elektrotechnik
BeziehungOrdentlicher Professor

NummerTitelECTSUmfangDozierende
227-0434-10LMathematics of Information Information 8 KP3V + 2U + 2AH. Bölcskei
KurzbeschreibungThe class focuses on mathematical aspects of

1. Information science: Sampling theorems, frame theory, compressed sensing, sparsity, super-resolution, spectrum-blind sampling, subspace algorithms, dimensionality reduction

2. Learning theory: Approximation theory, uniform laws of large numbers, Rademacher complexity, Vapnik-Chervonenkis dimension
LernzielThe aim of the class is to familiarize the students with the most commonly used mathematical theories in data science, high-dimensional data analysis, and learning theory. The class consists of the lecture, exercise sessions with homework problems, and of a research project, which can be carried out either individually or in groups. The research project consists of either 1. software development for the solution of a practical signal processing or machine learning problem or 2. the analysis of a research paper or 3. a theoretical research problem of suitable complexity. Students are welcome to propose their own project at the beginning of the semester. The outcomes of all projects have to be presented to the entire class at the end of the semester.
InhaltMathematics of Information

1. Signal representations: Frame theory, wavelets, Gabor expansions, sampling theorems, density theorems

2. Sparsity and compressed sensing: Sparse linear models, uncertainty relations in sparse signal recovery, matching pursuits, super-resolution, spectrum-blind sampling, subspace algorithms (MUSIC, ESPRIT, matrix pencil), estimation in the high-dimensional noisy case, Lasso

3. Dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma

Mathematics of Learning

4. Approximation theory: Nonlinear approximation theory, fundamental limits on compressibility of signal classes, Kolmogorov-Tikhomirov epsilon-entropy of signal classes, optimal compression of signal classes, recovery from incomplete data, information-based complexity, curse of dimensionality

5. Uniform laws of large numbers: Rademacher complexity, Vapnik-Chervonenkis dimension, classes with polynomial discrimination, blessings of dimensionality
SkriptDetailed lecture notes will be provided at the beginning of the semester and as we go along.
Voraussetzungen / BesonderesThis course is aimed at students with a background in basic linear algebra, analysis, statistics, and probability.

We encourage students who are interested in mathematical data science to take both this course and "401-4944-20L Mathematics of Data Science" by Prof. A. Bandeira. The two courses are designed to be complementary.

H. Bölcskei and A. Bandeira
401-5680-00LFoundations of Data Science Seminar Information 0 KPP. L. Bühlmann, A. Bandeira, H. Bölcskei, J. M. Buhmann, T. Hofmann, A. Krause, A. Lapidoth, H.‑A. Loeliger, M. H. Maathuis, N. Meinshausen, G. Rätsch, C. Uhler, S. van de Geer, F. Yang
KurzbeschreibungResearch colloquium
Lernziel