Suchergebnis: Katalogdaten im Frühjahrssemester 2021
Rechnergestützte Wissenschaften Master | ||||||
Kernfächer Von den angebotenen Kernfächern müssen mindestens zwei Lerneinheiten erfolgreich abgeschlossen werden. | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
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401-3632-00L | Computational Statistics | W | 8 KP | 3V + 1U | M. Mächler | |
Kurzbeschreibung | We discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R. | |||||
Lernziel | The student obtains an overview of modern statistical methods for data analysis, including their algorithmic aspects and theoretical properties. The methods are applied using the statistical programming language R. | |||||
Inhalt | See the class website | |||||
Voraussetzungen / Besonderes | At least one semester of (basic) probability and statistics. Programming experience is helpful but not required. | |||||
263-0007-00L | Advanced Systems Lab Only for master students, otherwise a special permission by the study administration of D-INFK is required. | W | 8 KP | 3V + 2U + 2A | M. Püschel, C. Zhang | |
Kurzbeschreibung | This course introduces the student to the foundations and state-of-the-art techniques in developing high performance software for mathematical functionality occurring in various fields in computer science. The focus is on optimizing for a single core and includes optimizing for the memory hierarchy, for special instruction sets, and the possible use of automatic performance tuning. | |||||
Lernziel | Software performance (i.e., runtime) arises through the complex interaction of algorithm, its implementation, the compiler used, and the microarchitecture the program is run on. The first goal of the course is to provide the student with an understanding of this "vertical" interaction, and hence software performance, for mathematical functionality. The second goal is to teach a systematic strategy how to use this knowledge to write fast software for numerical problems. This strategy will be trained in several homeworks and a semester-long group project. | |||||
Inhalt | The fast evolution and increasing complexity of computing platforms pose a major challenge for developers of high performance software for engineering, science, and consumer applications: it becomes increasingly harder to harness the available computing power. Straightforward implementations may lose as much as one or two orders of magnitude in performance. On the other hand, creating optimal implementations requires the developer to have an understanding of algorithms, capabilities and limitations of compilers, and the target platform's architecture and microarchitecture. This interdisciplinary course introduces the student to the foundations and state-of-the-art techniques in high performance mathematical software development using important functionality such as matrix operations, transforms, filters, and others as examples. The course will explain how to optimize for the memory hierarchy, take advantage of special instruction sets, and other details of current processors that require optimization. The concept of automatic performance tuning is introduced. The focus is on optimization for a single core; thus, the course complements others on parallel and distributed computing. Finally a general strategy for performance analysis and optimization is introduced that the students will apply in group projects that accompany the course. | |||||
Voraussetzungen / Besonderes | Solid knowledge of the C programming language and matrix algebra. | |||||
261-5110-00L | Optimization for Data Science | W | 10 KP | 3V + 2U + 4A | B. Gärtner, D. Steurer, N. He | |
Kurzbeschreibung | This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in data science. | |||||
Lernziel | Understanding the theoretical guarantees (and their limits) of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science. | |||||
Inhalt | This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in machine learning and data science. In the first part of the course, we will first give a brief introduction to convex optimization, with some basic motivating examples from machine learning. Then we will analyse classical and more recent first and second order methods for convex optimization: gradient descent, Nesterov's accelerated method, proximal and splitting algorithms, subgradient descent, stochastic gradient descent, variance-reduced methods, Newton's method, and Quasi-Newton methods. The emphasis will be on analysis techniques that occur repeatedly in convergence analyses for various classes of convex functions. We will also discuss some classical and recent theoretical results for nonconvex optimization. In the second part, we discuss convex programming relaxations as a powerful and versatile paradigm for designing efficient algorithms to solve computational problems arising in data science. We will learn about this paradigm and develop a unified perspective on it through the lens of the sum-of-squares semidefinite programming hierarchy. As applications, we are discussing non-negative matrix factorization, compressed sensing and sparse linear regression, matrix completion and phase retrieval, as well as robust estimation. | |||||
Voraussetzungen / Besonderes | As background, we require material taught in the course "252-0209-00L Algorithms, Probability, and Computing". It is not necessary that participants have actually taken the course, but they should be prepared to catch up if necessary. |
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