Search result: Catalogue data in Autumn Semester 2019
Data Science Master  | ||||||
 Core Courses | ||||||
| Core Electives | ||||||
| Number | Title | Type | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|---|
| 401-3627-00L | High-Dimensional Statistics | W | 4 credits | 2V | P. L. Bühlmann | |
| Abstract | "High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed. | |||||
| Learning objective | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||
| Content | Lasso and Group Lasso for high-dimensional linear and generalized linear models; Additive models and many smooth univariate functions; Non-convex loss functions and l1-regularization; Stability selection, multiple testing and construction of p-values; Undirected graphical modeling | |||||
| Literature | Peter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag. ISBN 978-3-642-20191-2. | |||||
| Prerequisites / Notice | Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics). | |||||
| 401-3901-00L | Mathematical Optimization | W | 11 credits | 4V + 2U | R. Zenklusen | |
| Abstract | Mathematical treatment of diverse optimization techniques. | |||||
| Learning objective | The goal of this course is to get a thorough understanding of various classical mathematical optimization techniques with an emphasis on polyhedral approaches. In particular, we want students to develop a good understanding of some important problem classes in the field, of structural mathematical results linked to these problems, and of solution approaches based on this structural understanding. | |||||
| Content | Key topics include: - Linear programming and polyhedra; - Flows and cuts; - Combinatorial optimization problems and techniques; - Equivalence between optimization and separation; - Brief introduction to Integer Programming. | |||||
| Literature | - Bernhard Korte, Jens Vygen: Combinatorial Optimization. 6th edition, Springer, 2018. - Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency. Springer, 2003. This work has 3 volumes. - Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993. - Alexander Schrijver: Theory of Linear and Integer Programming. John Wiley, 1986. | |||||
| Prerequisites / Notice | Solid background in linear algebra. | |||||
| 401-3612-00L | Stochastic Simulation Does not take place this semester. | W | 5 credits | 3G | ||
| Abstract | This course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo. | |||||
| Learning objective | Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R. | |||||
| Content | Examples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC). | |||||
| Lecture notes | A script will be available in English. | |||||
| Literature | P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer 2004. B. D. Ripley. Stochastic Simulation. Wiley, 1987. Ch. Robert, G. Casella. Monte Carlo Statistical Methods. Springer 2004 (2nd edition). | |||||
| Prerequisites / Notice | Familiarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed. | |||||
| 401-4619-67L | Advanced Topics in Computational Statistics Does not take place this semester. | W | 4 credits | 2V | not available | |
| Abstract | This lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling. | |||||
| Learning objective | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||
| Content | The main focus will be on graphical models in various forms: Markov properties of undirected graphs; Belief propagation; Hidden Markov Models; Structure estimation and parameter estimation; inference for high-dimensional data; causal graphical models | |||||
| Prerequisites / Notice | We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics. | |||||
| 401-4623-00L | Time Series Analysis Does not take place this semester. | W | 6 credits | 3G | N. Meinshausen | |
| Abstract | Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R. | |||||
| Learning objective | Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R. | |||||
| Content | This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations. Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R. | |||||
| Lecture notes | Not available | |||||
| Literature | A list of references will be distributed during the course. | |||||
| Prerequisites / Notice | Basic knowledge in probability and statistics | |||||
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