Name | Prof. Dr. Helmut Bölcskei |

Field | Mathematical Information Science |

Address | Professur Math. Informationswiss. ETH Zürich, ETF E 122 Sternwartstrasse 7 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 34 33 |

hboelcskei@ethz.ch | |

URL | https://www.mins.ee.ethz.ch/people/show/boelcskei |

Department | Information Technology and Electrical Engineering |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

227-0434-10L | Mathematics of Information | 8 credits | 3V + 2U + 2A | H. Bölcskei | |

Abstract | The 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, greedy algorithms, uniform laws of large numbers, Rademacher complexity, Vapnik-Chervonenkis dimension | ||||

Learning objective | The 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 and exercise sessions with homework problems. | ||||

Content | Mathematics 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, super-resolution, spectrum-blind sampling, subspace algorithms (ESPRIT), 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, best M-term approximation, greedy algorithms, fundamental limits on compressibility of signal classes, Kolmogorov-Tikhomirov epsilon-entropy of signal classes, optimal compression of signal classes 5. Uniform laws of large numbers: Rademacher complexity, Vapnik-Chervonenkis dimension, classes with polynomial discrimination | ||||

Lecture notes | Detailed lecture notes will be provided at the beginning of the semester. | ||||

Prerequisites / Notice | This 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 | ||||

401-5680-00L | Foundations of Data Science Seminar | 0 credits | P. L. Bühlmann, A. Bandeira, H. Bölcskei, S. van de Geer, F. Yang | ||

Abstract | Research colloquium | ||||

Learning objective |