Suchergebnis: Katalogdaten im Herbstsemester 2019

Data Science Master Information
Kernfächer
Datenanalyse
Information and Learning
NummerTitelTypECTSUmfangDozierende
252-0535-00LAdvanced Machine Learning Information W8 KP3V + 2U + 2AJ. M. Buhmann
KurzbeschreibungMachine learning algorithms provide analytical methods to search data sets for characteristic patterns. Typical tasks include the classification of data, function fitting and clustering, with applications in image and speech analysis, bioinformatics and exploratory data analysis. This course is accompanied by practical machine learning projects.
LernzielStudents will be familiarized with advanced concepts and algorithms for supervised and unsupervised learning; reinforce the statistics knowledge which is indispensible to solve modeling problems under uncertainty. Key concepts are the generalization ability of algorithms and systematic approaches to modeling and regularization. Machine learning projects will provide an opportunity to test the machine learning algorithms on real world data.
InhaltThe theory of fundamental machine learning concepts is presented in the lecture, and illustrated with relevant applications. Students can deepen their understanding by solving both pen-and-paper and programming exercises, where they implement and apply famous algorithms to real-world data.

Topics covered in the lecture include:

Fundamentals:
What is data?
Bayesian Learning
Computational learning theory

Supervised learning:
Ensembles: Bagging and Boosting
Max Margin methods
Neural networks

Unsupservised learning:
Dimensionality reduction techniques
Clustering
Mixture Models
Non-parametric density estimation
Learning Dynamical Systems
SkriptNo lecture notes, but slides will be made available on the course webpage.
LiteraturC. Bishop. Pattern Recognition and Machine Learning. Springer 2007.

R. Duda, P. Hart, and D. Stork. Pattern Classification. John Wiley &
Sons, second edition, 2001.

T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical
Learning: Data Mining, Inference and Prediction. Springer, 2001.

L. Wasserman. All of Statistics: A Concise Course in Statistical
Inference. Springer, 2004.
Voraussetzungen / BesonderesThe course requires solid basic knowledge in analysis, statistics and numerical methods for CSE as well as practical programming experience for solving assignments.
Students should have followed at least "Introduction to Machine Learning" or an equivalent course offered by another institution.

PhD students are required to obtain a passing grade in the course (4.0 or higher based on project and exam) to gain credit points.
227-0423-00LNeural Network TheoryW4 KP2V + 1UH. Bölcskei, E. Riegler
KurzbeschreibungThe class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks: Universal approximation theorems, capacity of separating surfaces, generalization, reproducing Kernel Hilbert spaces, support vector machines, fundamental limits of deep neural network learning, dimension measures, feature extraction with scattering networks
LernzielAfter attending this lecture, participating in the exercise sessions, and working on the homework problem sets, students will have acquired a working knowledge of the mathematical foundations of neural networks.
Inhalt1. Universal approximation with single- and multi-layer networks

2. Geometry of decision surfaces

3. Separating capacity of nonlinear decision surfaces

4. Generalization

5. Reproducing Kernel Hilbert Spaces, support vector machines

6. Deep neural network approximation theory: Fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, covering numbers, fundamental limits of deep neural network learning

7. Learning of real-valued functions: Pseudo-dimension, fat-shattering dimension, Vapnik-Chervonenkis dimension

8. Scattering networks
SkriptDetailed lecture notes will be provided as we go along.
Voraussetzungen / BesonderesThis course is aimed at students with a strong mathematical background in general, and in linear algebra, analysis, and probability theory in particular.
Statistics
NummerTitelTypECTSUmfangDozierende
401-3621-00LFundamentals of Mathematical Statistics Information W10 KP4V + 1US. van de Geer
KurzbeschreibungThe course covers the basics of inferential statistics.
Lernziel
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