# Suchergebnis: Katalogdaten im Herbstsemester 2018

Data Science Master | ||||||

Kernfächer | ||||||

Datenanalyse | ||||||

Information and Learning | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|

252-0535-00L | Advanced Machine Learning | W | 8 KP | 3V + 2U + 2A | J. M. Buhmann | |

Kurzbeschreibung | Machine 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. | |||||

Lernziel | Students 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. | |||||

Inhalt | The 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 | |||||

Skript | No lecture notes, but slides will be made available on the course webpage. | |||||

Literatur | C. 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 / Besonderes | The 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. | |||||

Statistics | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |

401-3621-00L | Fundamentals of Mathematical Statistics | W | 10 KP | 4V + 1U | S. van de Geer | |

Kurzbeschreibung | The course covers the basics of inferential statistics. | |||||

Lernziel | ||||||

Datenmanagement und Datenverarbeitung | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |

263-3010-00L | Big Data | W | 8 KP | 3V + 2U + 2A | G. Fourny | |

Kurzbeschreibung | The key challenge of the information society is to turn data into information, information into knowledge, knowledge into value. This has become increasingly complex. Data comes in larger volumes, diverse shapes, from different sources. Data is more heterogeneous and less structured than forty years ago. Nevertheless, it still needs to be processed fast, with support for complex operations. | |||||

Lernziel | This combination of requirements, together with the technologies that have emerged in order to address them, is typically referred to as "Big Data." This revolution has led to a completely new way to do business, e.g., develop new products and business models, but also to do science -- which is sometimes referred to as data-driven science or the "fourth paradigm". Unfortunately, the quantity of data produced and available -- now in the Zettabyte range (that's 21 zeros) per year -- keeps growing faster than our ability to process it. Hence, new architectures and approaches for processing it were and are still needed. Harnessing them must involve a deep understanding of data not only in the large, but also in the small. The field of databases evolves at a fast pace. In order to be prepared, to the extent possible, to the (r)evolutions that will take place in the next few decades, the emphasis of the lecture will be on the paradigms and core design ideas, while today's technologies will serve as supporting illustrations thereof. After visiting this lecture, you should have gained an overview and understanding of the Big Data landscape, which is the basis on which one can make informed decisions, i.e., pick and orchestrate the relevant technologies together for addressing each business use case efficiently and consistently. | |||||

Inhalt | This course gives an overview of database technologies and of the most important database design principles that lay the foundations of the Big Data universe. The material is organized along three axes: data in the large, data in the small, data in the very small. A broad range of aspects is covered with a focus on how they fit all together in the big picture of the Big Data ecosystem. - physical storage: distributed file systems (HDFS), object storage(S3), key-value stores - logical storage: document stores (MongoDB), column stores (HBase), graph databases (neo4j), data warehouses (ROLAP) - data formats and syntaxes (XML, JSON, RDF, Turtle, CSV, XBRL, YAML, protocol buffers, Avro) - data shapes and models (tables, trees, graphs, cubes) - type systems and schemas: atomic types, structured types (arrays, maps), set-based type systems (?, *, +) - an overview of functional, declarative programming languages across data shapes (SQL, XQuery, JSONiq, Cypher, MDX) - the most important query paradigms (selection, projection, joining, grouping, ordering, windowing) - paradigms for parallel processing, two-stage (MapReduce) and DAG-based (Spark) - resource management (YARN) - what a data center is made of and why it matters (racks, nodes, ...) - underlying architectures (internal machinery of HDFS, HBase, Spark, neo4j) - optimization techniques (functional and declarative paradigms, query plans, rewrites, indexing) - applications. Large scale analytics and machine learning are outside of the scope of this course. | |||||

Literatur | Papers from scientific conferences and journals. References will be given as part of the course material during the semester. | |||||

Voraussetzungen / Besonderes | This course, in the autumn semester, is only intended for: - Computer Science students - Data Science students - CBB students with a Computer Science background Mobility students in CS are also welcome and encouraged to attend. If you experience any issue while registering, please contact the study administration and you will be gladly added. Another version of this course will be offered in Spring for students of other departments. However, if you would like to already start learning about databases now, a course worth taking as a preparation/good prequel to the Spring edition of Big Data is the "Information Systems for Engineers" course, offered this Fall for other departments as well, and introducing relational databases and SQL. | |||||

263-4500-10L | Advanced Algorithms (with Project) Only for Data Science MSc. | W | 8 KP | 2V + 2U + 2P + 1A | M. Ghaffari, A. Krause | |

Kurzbeschreibung | This is an advanced course on the design and analysis of algorithms, covering a range of topics and techniques not studied in typical introductory courses on algorithms. | |||||

Lernziel | This course is intended to familiarize students with (some of) the main tools and techniques developed over the last 15-20 years in algorithm design, which are by now among the key ingredients used in developing efficient algorithms. | |||||

Inhalt | the lectures will cover a range of topics, including the following: graph sparsifications while preserving cuts or distances, various approximation algorithms techniques and concepts, metric embeddings and probabilistic tree embeddings, online algorithms, multiplicative weight updates, streaming algorithms, sketching algorithms, and a bried glance at MapReduce algorithms. | |||||

Voraussetzungen / Besonderes | This course is designed for masters and doctoral students and it especially targets those interested in theoretical computer science, but it should also be accessible to last-year bachelor students. Sufficient comfort with both (A) Algorithm Design & Analysis and (B) Probability & Concentrations. E.g., having passed the course Algorithms, Probability, and Computing (APC) is highly recommended, though not required formally. If you are not sure whether you're ready for this class or not, please consulte the instructor. | |||||

Wählbare Kernfächer | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |

151-0563-01L | Dynamic Programming and Optimal Control | W | 4 KP | 2V + 1U | R. D'Andrea | |

Kurzbeschreibung | Introduction to Dynamic Programming and Optimal Control. | |||||

Lernziel | Covers the fundamental concepts of Dynamic Programming & Optimal Control. | |||||

Inhalt | Dynamic Programming Algorithm; Deterministic Systems and Shortest Path Problems; Infinite Horizon Problems, Bellman Equation; Deterministic Continuous-Time Optimal Control. | |||||

Literatur | Dynamic Programming and Optimal Control by Dimitri P. Bertsekas, Vol. I, 3rd edition, 2005, 558 pages, hardcover. | |||||

Voraussetzungen / Besonderes | Requirements: Knowledge of advanced calculus, introductory probability theory, and matrix-vector algebra. | |||||

252-0417-00L | Randomized Algorithms and Probabilistic Methods | W | 8 KP | 3V + 2U + 2A | A. Steger | |

Kurzbeschreibung | Las Vegas & Monte Carlo algorithms; inequalities of Markov, Chebyshev, Chernoff; negative correlation; Markov chains: convergence, rapidly mixing; generating functions; Examples include: min cut, median, balls and bins, routing in hypercubes, 3SAT, card shuffling, random walks | |||||

Lernziel | After this course students will know fundamental techniques from probabilistic combinatorics for designing randomized algorithms and will be able to apply them to solve typical problems in these areas. | |||||

Inhalt | Randomized Algorithms are algorithms that "flip coins" to take certain decisions. This concept extends the classical model of deterministic algorithms and has become very popular and useful within the last twenty years. In many cases, randomized algorithms are faster, simpler or just more elegant than deterministic ones. In the course, we will discuss basic principles and techniques and derive from them a number of randomized methods for problems in different areas. | |||||

Skript | Yes. | |||||

Literatur | - Randomized Algorithms, Rajeev Motwani and Prabhakar Raghavan, Cambridge University Press (1995) - Probability and Computing, Michael Mitzenmacher and Eli Upfal, Cambridge University Press (2005) | |||||

252-1414-00L | System Security | W | 5 KP | 2V + 2U | S. Capkun, A. Perrig | |

Kurzbeschreibung | The first part of the lecture covers individual system aspects starting with tamperproof or tamper-resistant hardware in general over operating system related security mechanisms to application software systems, such as host based intrusion detection systems. In the second part, the focus is on system design and methodologies for building secure systems. | |||||

Lernziel | In this lecture, students learn about the security requirements and capabilities that are expected from modern hardware, operating systems, and other software environments. An overview of available technologies, algorithms and standards is given, with which these requirements can be met. | |||||

Inhalt | The first part of the lecture covers individual system's aspects starting with tamperproof or tamperresistant hardware in general over operating system related security mechanisms to application software systems such as host based intrusion detetction systems. The main topics covered are: tamper resistant hardware, CPU support for security, protection mechanisms in the kernel, file system security (permissions / ACLs / network filesystem issues), IPC Security, mechanisms in more modern OS, such as Capabilities and Zones, Libraries and Software tools for security assurance, etc. In the second part, the focus is on system design and methodologies for building secure systems. Topics include: patch management, common software faults (buffer overflows, etc.), writing secure software (design, architecture, QA, testing), compiler-supported security, language-supported security, logging and auditing (BSM audit, dtrace, ...), cryptographic support, and trustworthy computing (TCG, SGX). Along the lectures, model cases will be elaborated and evaluated in the exercises. | |||||

261-5130-00L | Research in Data Science | W | 6 KP | 13A | Professor/innen | |

Kurzbeschreibung | Independent work under the supervision of a core or adjunct faculty of data science. | |||||

Lernziel | Independent work under the supervision of a core or adjunct faculty of data science. An approval of the director of studies is required for a non DS professor. | |||||

Inhalt | Project done under supervision of an approved professor. | |||||

Voraussetzungen / Besonderes | Only students who have passed at least one core course in Data Management and Processing, and one core course in Data Analysis can start with a research project. A project description must be submitted at the start of the project to the studies administration. | |||||

263-0006-00L | Algorithms LabOnly for master students, otherwise a special permission by the student administration of D-INFK is required. | W | 8 KP | 4P + 3A | A. Steger, E. Welzl, P. Widmayer | |

Kurzbeschreibung | Students learn how to solve algorithmic problems given by a textual description (understanding problem setting, finding appropriate modeling, choosing suitable algorithms, and implementing them). Knowledge of basic algorithms and data structures is assumed; more advanced material and usage of standard libraries for combinatorial algorithms are introduced in tutorials. | |||||

Lernziel | The objective of this course is to learn how to solve algorithmic problems given by a textual description. This includes appropriate problem modeling, choice of suitable (combinatorial) algorithms, and implementing them (using C/C++, STL, CGAL, and BGL). | |||||

Literatur | T. Cormen, C. Leiserson, R. Rivest: Introduction to Algorithms, MIT Press, 1990. J. Hromkovic, Teubner: Theoretische Informatik, Springer, 2004 (English: Theoretical Computer Science, Springer 2003). J. Kleinberg, É. Tardos: Algorithm Design, Addison Wesley, 2006. H. R. Lewis, C. H. Papadimitriou: Elements of the Theory of Computation, Prentice Hall, 1998. T. Ottmann, P. Widmayer: Algorithmen und Datenstrukturen, Spektrum, 2012. R. Sedgewick: Algorithms in C++: Graph Algorithms, Addison-Wesley, 2001. | |||||

263-0007-00L | Advanced Systems Lab Only for master students, otherwise a special permission by the student administration of D-INFK is required. | W | 8 KP | 4P + 3A | G. Alonso | |

Kurzbeschreibung | The goal of this course is to teach students how to evaluate the performance of complex computer and software systems. Accordingly, the methodology to carry out experiments and measurements is studied. Furthermore, the modelling of systems with the help of queueing network systems is explained. | |||||

Lernziel | The goal of this course is to teach students how to evaluate the performance of complex computer and software systems. | |||||

263-2400-00L | Reliable and Interpretable Artificial Intelligence | W | 4 KP | 2V + 1U | M. Vechev | |

Kurzbeschreibung | Creating reliable and explainable probabilistic models is a fundamental challenge to solving the artificial intelligence problem. This course covers some of the latest and most exciting advances that bring us closer to constructing such models. | |||||

Lernziel | The main objective of this course is to expose students to the latest and most exciting research in the area of explainable and interpretable artificial intelligence, a topic of fundamental and increasing importance. Upon completion of the course, the students should have mastered the underlying methods and be able to apply them to a variety of problems. To facilitate deeper understanding, an important part of the course will be a group hands-on programming project where students will build a system based on the learned material. | |||||

Inhalt | The course covers the following inter-connected directions. Part I: Robust and Explainable Deep Learning ------------------------------------------------------------- Deep learning technology has made impressive advances in recent years. Despite this progress however, the fundamental challenge with deep learning remains that of understanding what a trained neural network has actually learned, and how stable that solution is. Forr example: is the network stable to slight perturbations of the input (e.g., an image)? How easy it is to fool the network into mis-classifying obvious inputs? Can we guide the network in a manner beyond simple labeled data? Topics: - Attacks: Finding adversarial examples via state-of-the-art attacks (e.g., FGSM, PGD attacks). - Defenses: Automated methods and tools which guarantee robustness of deep nets (e.g., using abstract domains, mixed-integer solvers) - Combing differentiable logic with gradient-based methods so to train networks to satisfy richer properties. - Frameworks: AI2, DiffAI, Reluplex, DQL, DeepPoly, etc. Part II: Program Synthesis/Induction ------------------------------------------------ Synthesis is a new frontier in AI where the computer programs itself via user provided examples. Synthesis has significant applications for non-programmers as well as for programmers where it can provide massive productivity increase (e.g., wrangling for data scientists). Modern synthesis techniques excel at learning functions over discrete spaces from (partial) intent. There have been a number of recent, exciting breakthroughs in techniques that discover complex, interpretable/explainable functions from few examples, partial sketches and other forms of supervision. Topics: - Theory of program synthesis: version spaces, counter-example guided inductive synthesis (CEGIS) with SAT/SMT, lower bounds on learning. - Applications of techniques: synthesis for end users (e.g., spreadsheets) and data analytics. - Combining synthesis with learning: application to learning from code. - Frameworks: PHOG, DeepCode. Part III: Probabilistic Programming ---------------------------------------------- Probabilistic programming is an emerging direction, recently also pushed by various companies (e.g., Facebook, Uber, Google) whose goal is democratize the construction of probabilistic models. In probabilistic programming, the user specifies a model while inference is left to the underlying solver. The idea is that the higher level of abstraction makes it easier to express, understand and reason about probabilistic models. Topics: - Probabilistic Inference: sampling based, exact symbolic inference, semantics - Applications of probabilistic programming: bias in deep learning, differential privacy (connects to Part I). - Frameworks: PSI, Edward2, Venture. | |||||

Voraussetzungen / Besonderes | The course material is self-contained: needed background is covered in the lectures and exercises, and additional pointers. | |||||

263-2800-00L | Design of Parallel and High-Performance Computing | W | 7 KP | 3V + 2U + 1A | T. Hoefler, M. Püschel | |

Kurzbeschreibung | Advanced topics in parallel / concurrent programming. | |||||

Lernziel | Understand concurrency paradigms and models from a higher perspective and acquire skills for designing, structuring and developing possibly large concurrent software systems. Become able to distinguish parallelism in problem space and in machine space. Become familiar with important technical concepts and with concurrency folklore. | |||||

263-3210-00L | Deep Learning Maximale Teilnehmerzahl: 300 | W | 4 KP | 2V + 1U | F. Perez Cruz | |

Kurzbeschreibung | Deep learning is an area within machine learning that deals with algorithms and models that automatically induce multi-level data representations. | |||||

Lernziel | In recent years, deep learning and deep networks have significantly improved the state-of-the-art in many application domains such as computer vision, speech recognition, and natural language processing. This class will cover the mathematical foundations of deep learning and provide insights into model design, training, and validation. The main objective is a profound understanding of why these methods work and how. There will also be a rich set of hands-on tasks and practical projects to familiarize students with this emerging technology. | |||||

Voraussetzungen / Besonderes | This is an advanced level course that requires some basic background in machine learning. More importantly, students are expected to have a very solid mathematical foundation, including linear algebra, multivariate calculus, and probability. The course will make heavy use of mathematics and is not (!) meant to be an extended tutorial of how to train deep networks with tools like Torch or Tensorflow, although that may be a side benefit. The participation in the course is subject to the following conditions: 1) The number of participants is limited to 300 students (MSc and PhDs). 2) Students must have taken the exam in Machine Learning (252-0535-00) or have acquired equivalent knowledge, see exhaustive list below: Machine Learning Link Computational Intelligence Lab Link Learning and Intelligent Systems/Introduction to Machine Learning Link Statistical Learning Theory Link Computational Statistics Link Probabilistic Artificial Intelligence Link Data Mining: Learning from Large Data Sets Link | |||||

263-5210-00L | Probabilistic Artificial Intelligence | W | 4 KP | 2V + 1U | A. Krause | |

Kurzbeschreibung | This course introduces core modeling techniques and algorithms from statistics, optimization, planning, and control and study applications in areas such as sensor networks, robotics, and the Internet. | |||||

Lernziel | How can we build systems that perform well in uncertain environments and unforeseen situations? How can we develop systems that exhibit "intelligent" behavior, without prescribing explicit rules? How can we build systems that learn from experience in order to improve their performance? We will study core modeling techniques and algorithms from statistics, optimization, planning, and control and study applications in areas such as sensor networks, robotics, and the Internet. The course is designed for upper-level undergraduate and graduate students. | |||||

Inhalt | Topics covered: - Search (BFS, DFS, A*), constraint satisfaction and optimization - Tutorial in logic (propositional, first-order) - Probability - Bayesian Networks (models, exact and approximative inference, learning) - Temporal models (Hidden Markov Models, Dynamic Bayesian Networks) - Probabilistic palnning (MDPs, POMPDPs) - Reinforcement learning - Combining logic and probability | |||||

Voraussetzungen / Besonderes | Solid basic knowledge in statistics, algorithms and programming | |||||

263-5902-00L | Computer Vision | W | 6 KP | 3V + 1U + 1A | M. Pollefeys, V. Ferrari, L. Van Gool | |

Kurzbeschreibung | The goal of this course is to provide students with a good understanding of computer vision and image analysis techniques. The main concepts and techniques will be studied in depth and practical algorithms and approaches will be discussed and explored through the exercises. | |||||

Lernziel | The objectives of this course are: 1. To introduce the fundamental problems of computer vision. 2. To introduce the main concepts and techniques used to solve those. 3. To enable participants to implement solutions for reasonably complex problems. 4. To enable participants to make sense of the computer vision literature. | |||||

Inhalt | Camera models and calibration, invariant features, Multiple-view geometry, Model fitting, Stereo Matching, Segmentation, 2D Shape matching, Shape from Silhouettes, Optical flow, Structure from motion, Tracking, Object recognition, Object category recognition | |||||

Voraussetzungen / Besonderes | It is recommended that students have taken the Visual Computing lecture or a similar course introducing basic image processing concepts before taking this course. | |||||

401-0625-01L | Applied Analysis of Variance and Experimental Design | W | 5 KP | 2V + 1U | L. Meier | |

Kurzbeschreibung | Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power. | |||||

Lernziel | Participants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R. | |||||

Inhalt | Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power. | |||||

Literatur | G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000. | |||||

Voraussetzungen / Besonderes | The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held. | |||||

401-3054-14L | Probabilistic Methods in Combinatorics | W | 6 KP | 2V + 1U | B. Sudakov | |

Kurzbeschreibung | This course provides a gentle introduction to the Probabilistic Method, with an emphasis on methodology. We will try to illustrate the main ideas by showing the application of probabilistic reasoning to various combinatorial problems. | |||||

Lernziel | ||||||

Inhalt | The topics covered in the class will include (but are not limited to): linearity of expectation, the second moment method, the local lemma, correlation inequalities, martingales, large deviation inequalities, Janson and Talagrand inequalities and pseudo-randomness. | |||||

Literatur | - The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008. - Random Graphs, by B. Bollobás, 2nd Edition, Cambridge University Press, 2001. - Random Graphs, by S. Janson, T. Luczak and A. Rucinski, Wiley, 2000. - Graph Coloring and the Probabilistic Method, by M. Molloy and B. Reed, Springer, 2002. | |||||

401-3601-00L | Probability Theory Höchstens eines der drei Bachelor-Kernfächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist im Master-Studiengang Mathematik anrechenbar. | W | 10 KP | 4V + 1U | A.‑S. Sznitman | |

Kurzbeschreibung | Basics of probability theory and the theory of stochastic processes in discrete time | |||||

Lernziel | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||

Inhalt | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||

Skript | available, will be sold in the course | |||||

Literatur | R. Durrett, Probability: Theory and examples, Duxbury Press 1996 H. Bauer, Probability Theory, de Gruyter 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 D. Williams, Probability with martingales, Cambridge University Press 1991 | |||||

401-3612-00L | Stochastic Simulation | W | 5 KP | 3G | F. Sigrist | |

Kurzbeschreibung | 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. | |||||

Lernziel | 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. | |||||

Inhalt | 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). | |||||

Skript | A script will be available in English. | |||||

Literatur | 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). | |||||

Voraussetzungen / Besonderes | Familiarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed. | |||||

401-3627-00L | High-Dimensional StatisticsFindet dieses Semester nicht statt. | W | 4 KP | 2V | P. L. Bühlmann | |

Kurzbeschreibung | "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. | |||||

Lernziel | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||

Inhalt | 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 | |||||

Literatur | 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. | |||||

Voraussetzungen / Besonderes | Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics). |

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