# Suchergebnis: Katalogdaten im Frühjahrssemester 2021

Data Science Master | ||||||

Kernfächer | ||||||

Wählbare Kernfächer | ||||||

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

263-0008-00L | Computational Intelligence Lab Only for master students, otherwise a special permission by the study administration of D-INFK is required. | W | 8 KP | 2V + 2U + 3A | T. Hofmann | |

Kurzbeschreibung | This laboratory course teaches fundamental concepts in computational science and machine learning with a special emphasis on matrix factorization and representation learning. The class covers techniques like dimension reduction, data clustering, sparse coding, and deep learning as well as a wide spectrum of related use cases and applications. | |||||

Lernziel | Students acquire fundamental theoretical concepts and methodologies from machine learning and how to apply these techniques to build intelligent systems that solve real-world problems. They learn to successfully develop solutions to application problems by following the key steps of modeling, algorithm design, implementation and experimental validation. This lab course has a strong focus on practical assignments. Students work in groups of three to four people, to develop solutions to three application problems: 1. Collaborative filtering and recommender systems, 2. Text sentiment classification, and 3. Road segmentation in aerial imagery. For each of these problems, students submit their solutions to an online evaluation and ranking system, and get feedback in terms of numerical accuracy and computational speed. In the final part of the course, students combine and extend one of their previous promising solutions, and write up their findings in an extended abstract in the style of a conference paper. (Disclaimer: The offered projects may be subject to change from year to year.) | |||||

Inhalt | see course description | |||||

263-2925-00L | Program Analysis for System Security and Reliability | W | 7 KP | 2V + 1U + 3A | M. Vechev | |

Kurzbeschreibung | Security issues in modern systems (blockchains, datacenters, deep learning, etc.) result in billions of losses due to hacks and system downtime. This course introduces fundamental techniques (ranging from automated analysis, machine learning, synthesis, zero-knowledge and their combinations) that can be applied in practice so to build more secure and reliable modern systems. | |||||

Lernziel | * Understand the fundamental techniques used to create modern security and reliability analysis engines that are used worldwide. * Understand how symbolic techniques are combined with machine learning (e.g., deep learning, reinforcement learning) so to create new kinds of learning-based analyzers. * Understand how to quantify and fix security and reliability issues in modern deep learning models. * Understand open research questions from both theoretical and practical perspectives. | |||||

Inhalt | Please see: https://www.sri.inf.ethz.ch/teaching/pass2021 for detailed course content. | |||||

263-3710-00L | Machine Perception Number of participants limited to 200. | W | 8 KP | 3V + 2U + 2A | O. Hilliges, S. Tang | |

Kurzbeschreibung | Recent developments in neural networks (aka “deep learning”) have drastically advanced the performance of machine perception systems in a variety of areas including computer vision, robotics, and intelligent UIs. This course is a deep dive into deep learning algorithms and architectures with applications to a variety of perceptual tasks. | |||||

Lernziel | Students will learn about fundamental aspects of modern deep learning approaches for perception. Students will learn to implement, train and debug their own neural networks and gain a detailed understanding of cutting-edge research in learning-based computer vision, robotics and HCI. The final project assignment will involve training a complex neural network architecture and applying it on a real-world dataset of human activity. The core competency acquired through this course is a solid foundation in deep-learning algorithms to process and interpret human input into computing systems. In particular, students should be able to develop systems that deal with the problem of recognizing people in images, detecting and describing body parts, inferring their spatial configuration, performing action/gesture recognition from still images or image sequences, also considering multi-modal data, among others. | |||||

Inhalt | We will focus on teaching: how to set up the problem of machine perception, the learning algorithms, network architectures and advanced deep learning concepts in particular probabilistic deep learning models The course covers the following main areas: I) Foundations of deep-learning. II) Probabilistic deep-learning for generative modelling of data (latent variable models, generative adversarial networks and auto-regressive models). III) Deep learning in computer vision, human-computer interaction and robotics. Specific topics include: I) Deep learning basics: a) Neural Networks and training (i.e., backpropagation) b) Feedforward Networks c) Timeseries modelling (RNN, GRU, LSTM) d) Convolutional Neural Networks for classification II) Probabilistic Deep Learning: a) Latent variable models (VAEs) b) Generative adversarial networks (GANs) c) Autoregressive models (PixelCNN, PixelRNN, TCNs) III) Deep Learning techniques for machine perception: a) Fully Convolutional architectures for dense per-pixel tasks (i.e., instance segmentation) b) Pose estimation and other tasks involving human activity c) Deep reinforcement learning IV) Case studies from research in computer vision, HCI, robotics and signal processing | |||||

Literatur | Deep Learning Book by Ian Goodfellow and Yoshua Bengio | |||||

Voraussetzungen / Besonderes | *** In accordance with the ETH Covid-19 master plan the lecture will be fully virtual. Details on the course website. *** This is an advanced grad-level course that requires a background in machine learning. Students are expected to have a solid mathematical foundation, in particular in linear algebra, multivariate calculus, and probability. The course will focus on state-of-the-art research in deep-learning and will not repeat basics of machine learning Please take note of the following conditions: 1) The number of participants is limited to 200 students (MSc and PhDs). 2) Students must have taken the exam in Machine Learning (252-0535-00) or have acquired equivalent knowledge 3) All practical exercises will require basic knowledge of Python and will use libraries such as Pytorch, scikit-learn and scikit-image. We will provide introductions to Pytorch and other libraries that are needed but will not provide introductions to basic programming or Python. The following courses are strongly recommended as prerequisite: * "Visual Computing" or "Computer Vision" The course will be assessed by a final written examination in English. No course materials or electronic devices can be used during the examination. Note that the examination will be based on the contents of the lectures, the associated reading materials and the exercises. | |||||

263-3855-00L | Cloud Computing Architecture | W | 9 KP | 3V + 2U + 3A | G. Alonso, A. Klimovic | |

Kurzbeschreibung | Cloud computing hosts a wide variety of online services that we use on a daily basis, including web search, social networks, and video streaming. This course will cover how datacenter hardware, systems software, and application frameworks are designed for the cloud. | |||||

Lernziel | After successful completion of this course, students will be able to: 1) reason about performance, energy efficiency, and availability tradeoffs in the design of cloud system software, 2) describe how datacenter hardware is organized and explain why it is organized as such, 3) implement cloud applications as well as analyze and optimize their performance. | |||||

Inhalt | In this course, we study how datacenter hardware, systems software, and applications are designed at large scale for the cloud. The course covers topics including server design, cluster management, large-scale storage systems, serverless computing, data analytics frameworks, and performance analysis. | |||||

Skript | Lecture slides will be available on the course website. | |||||

Voraussetzungen / Besonderes | Undergraduate courses in 1) computer architecture and 2) operating systems, distributed systems, and/or database systems are strongly recommended. | |||||

263-4400-00L | Advanced Graph Algorithms and Optimization | W | 8 KP | 3V + 1U + 3A | R. Kyng, M. Probst | |

Kurzbeschreibung | This course will cover a number of advanced topics in optimization and graph algorithms. | |||||

Lernziel | The course will take students on a deep dive into modern approaches to graph algorithms using convex optimization techniques. By studying convex optimization through the lens of graph algorithms, students should develop a deeper understanding of fundamental phenomena in optimization. The course will cover some traditional discrete approaches to various graph problems, especially flow problems, and then contrast these approaches with modern, asymptotically faster methods based on combining convex optimization with spectral and combinatorial graph theory. | |||||

Inhalt | Students should leave the course understanding key concepts in optimization such as first and second-order optimization, convex duality, multiplicative weights and dual-based methods, acceleration, preconditioning, and non-Euclidean optimization. Students will also be familiarized with central techniques in the development of graph algorithms in the past 15 years, including graph decomposition techniques, sparsification, oblivious routing, and spectral and combinatorial preconditioning. | |||||

Voraussetzungen / Besonderes | This course is targeted toward masters and doctoral students with an interest in theoretical computer science. Students should be comfortable with design and analysis of algorithms, probability, and linear algebra. Having passed the course Algorithms, Probability, and Computing (APC) is highly recommended, but not formally required. If you are not sure whether you're ready for this class or not, please consult the instructor. | |||||

263-5000-00L | Computational Semantics for Natural Language Processing Limited number of participants: 80. Last cancellation/deregistration date for this graded semester performance: Friday, 26 March 2021! Please note that after that date no deregistration will be accepted and the course will be considered as "fail". | W | 6 KP | 2V + 1U + 2A | M. Sachan | |

Kurzbeschreibung | This course presents an introduction to Natural language processing (NLP) with an emphasis on computational semantics i.e. the process of constructing and reasoning with meaning representations of natural language text. | |||||

Lernziel | The objective of the course is to learn about various topics in computational semantics and its importance in natural language processing methodology and research. Exercises and the project will be key parts of the course so the students will be able to gain hands-on experience with state-of-the-art techniques in the field. | |||||

Inhalt | We will take a modern view of the topic, and focus on various statistical and deep learning approaches for computation semantics. We will also overview various primary areas of research in language processing and discuss how the computational semantics view can help us make advances in NLP. | |||||

Skript | Lecture slides will be made available at the course Web site. | |||||

Literatur | No textbook is required, but there will be regularly assigned readings from research literature, linked to the course website. | |||||

Voraussetzungen / Besonderes | The student should have successfully completed a graduate level class in machine learning (252-0220-00L), deep learning (263-3210-00L) or natural language processing (252-3005-00L) before. Similar courses from other universities are acceptable too. | |||||

263-5300-00L | Guarantees for Machine Learning Number of participants limited to 30. Last cancellation/deregistration date for this graded semester performance: 17 March 2021! Please note that after that date no deregistration will be accepted and a "no show" will appear on your transcript. | W | 7 KP | 3G + 3A | F. Yang | |

Kurzbeschreibung | This course is aimed at advanced master and doctorate students who want to conduct independent research on theory for modern machine learning (ML). It teaches classical and recent methods in statistical learning theory commonly used to prove theoretical guarantees for ML algorithms. The knowledge is then applied in independent project work that focuses on understanding modern ML phenomena. | |||||

Lernziel | Learning objectives: - acquire enough mathematical background to understand a good fraction of theory papers published in the typical ML venues. For this purpose, students will learn common mathematical techniques from statistics and optimization in the first part of the course and apply this knowledge in the project work - critically examine recently published work in terms of relevance and determine impactful (novel) research problems. This will be an integral part of the project work and involves experimental as well as theoretical questions - find and outline an approach (some subproblem) to prove a conjectured theorem. This will be practiced in lectures / exercise and homeworks and potentially in the final project. - effectively communicate and present the problem motivation, new insights and results to a technical audience. This will be primarily learned via the final presentation and report as well as during peer-grading of peer talks. | |||||

Inhalt | This course touches upon foundational methods in statistical learning theory aimed at proving theoretical guarantees for machine learning algorithms, touching on the following topics - concentration bounds - uniform convergence and empirical process theory - high-dimensional statistics (e.g. sparsity) - regularization for non-parametric statistics (e.g. in RKHS, neural networks) - implicit regularization via gradient descent (e.g. margins, early stopping) - minimax lower bounds The project work focuses on current theoretical ML research that aims to understand modern phenomena in machine learning, including but not limited to - how overparameterization could help generalization ( RKHS, NN ) - how overparameterization could help optimization ( non-convex optimization, loss landscape ) - complexity measures and approximation theoretic properties of randomly initialized and trained NN - generalization of robust learning ( adversarial robustness, standard and robust error tradeoff, distribution shift) | |||||

Voraussetzungen / Besonderes | It’s absolutely necessary for students to have a strong mathematical background (basic real analysis, probability theory, linear algebra) and good knowledge of core concepts in machine learning taught in courses such as “Introduction to Machine Learning”, “Regression”/ “Statistical Modelling”. In addition to these prerequisites, this class requires a high degree of mathematical maturity—including abstract thinking and the ability to understand and write proofs. Students have usually taken a subset of Fundamentals of Mathematical Statistics, Probabilistic AI, Neural Network Theory, Optimization for Data Science, Advanced ML, Statistical Learning Theory, Probability Theory (D-MATH) | |||||

401-0674-00L | Numerical Methods for Partial Differential EquationsNicht für Studierende BSc/MSc Mathematik | W | 10 KP | 2G + 2U + 2P + 4A | R. Hiptmair | |

Kurzbeschreibung | Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations: convection-diffusion, heat equation, wave equation, conservation laws. Implementation in C++ based on a finite element library. | |||||

Lernziel | Main skills to be acquired in this course: * Ability to implement fundamental numerical methods for the solution of partial differential equations efficiently. * Ability to modify and adapt numerical algorithms guided by awareness of their mathematical foundations. * Ability to select and assess numerical methods in light of the predictions of theory * Ability to identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm. * Ability to understand research publications on theoretical and practical aspects of numerical methods for partial differential equations. * Skills in the efficient implementation of finite element methods on unstructured meshes. This course is neither a course on the mathematical foundations and numerical analysis of methods nor an course that merely teaches recipes and how to apply software packages. | |||||

Inhalt | 1 Second-Order Scalar Elliptic Boundary Value Problems 1.2 Equilibrium Models: Examples 1.3 Sobolev spaces 1.4 Linear Variational Problems 1.5 Equilibrium Models: Boundary Value Problems 1.6 Diffusion Models (Stationary Heat Conduction) 1.7 Boundary Conditions 1.8 Second-Order Elliptic Variational Problems 1.9 Essential and Natural Boundary Conditions 2 Finite Element Methods (FEM) 2.2 Principles of Galerkin Discretization 2.3 Case Study: Linear FEM for Two-Point Boundary Value Problems 2.4 Case Study: Triangular Linear FEM in Two Dimensions 2.5 Building Blocks of General Finite Element Methods 2.6 Lagrangian Finite Element Methods 2.7 Implementation of Finite Element Methods 2.7.1 Mesh Generation and Mesh File Format 2.7.2 Mesh Information and Mesh Data Structures 2.7.2.1 L EHR FEM++ Mesh: Container Layer 2.7.2.2 L EHR FEM++ Mesh: Topology Layer 2.7.2.3 L EHR FEM++ Mesh: Geometry Layer 2.7.3 Vectors and Matrices 2.7.4 Assembly Algorithms 2.7.4.1 Assembly: Localization 2.7.4.2 Assembly: Index Mappings 2.7.4.3 Distribute Assembly Schemes 2.7.4.4 Assembly: Linear Algebra Perspective 2.7.5 Local Computations 2.7.5.1 Analytic Formulas for Entries of Element Matrices 2.7.5.2 Local Quadrature 2.7.6 Treatment of Essential Boundary Conditions 2.8 Parametric Finite Element Methods 3 FEM: Convergence and Accuracy 3.1 Abstract Galerkin Error Estimates 3.2 Empirical (Asymptotic) Convergence of Lagrangian FEM 3.3 A Priori (Asymptotic) Finite Element Error Estimates 3.4 Elliptic Regularity Theory 3.5 Variational Crimes 3.6 FEM: Duality Techniques for Error Estimation 3.7 Discrete Maximum Principle 3.8 Validation and Debugging of Finite Element Codes 4 Beyond FEM: Alternative Discretizations [dropped] 5 Non-Linear Elliptic Boundary Value Problems [dropped] 6 Second-Order Linear Evolution Problems 6.1 Time-Dependent Boundary Value Problems 6.2 Parabolic Initial-Boundary Value Problems 6.3 Linear Wave Equations 7 Convection-Diffusion Problems [dropped] 8 Numerical Methods for Conservation Laws 8.1 Conservation Laws: Examples 8.2 Scalar Conservation Laws in 1D 8.3 Conservative Finite Volume (FV) Discretization 8.4 Timestepping for Finite-Volume Methods 8.5 Higher-Order Conservative Finite-Volume Schemes | |||||

Skript | The lecture will be taught in flipped classroom format: - Video tutorials for all thematic units will be published online. - Tablet notes accompanying the videos will be made available to the audience as PDF. - A comprehensive lecture document will cover all aspects of the course. | |||||

Literatur | Chapters of the following books provide supplementary reading (detailed references in course material): * D. Braess: Finite Elemente, Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Springer 2007 (available online). * S. Brenner and R. Scott. Mathematical theory of finite element methods, Springer 2008 (available online). * A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer, New York, 2004. * Ch. Großmann and H.-G. Roos: Numerical Treatment of Partial Differential Equations, Springer 2007. * W. Hackbusch. Elliptic Differential Equations. Theory and Numerical Treatment, volume 18 of Springer Series in Computational Mathematics. Springer, Berlin, 1992. * P. Knabner and L. Angermann. Numerical Methods for Elliptic and Parabolic Partial Differential Equations, volume 44 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * S. Larsson and V. Thomée. Partial Differential Equations with Numerical Methods, volume 45 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * R. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK, 2002. However, study of supplementary literature is not important for for following the course. | |||||

Voraussetzungen / Besonderes | Mastery of basic calculus and linear algebra is taken for granted. Familiarity with fundamental numerical methods (solution methods for linear systems of equations, interpolation, approximation, numerical quadrature, numerical integration of ODEs) is essential. Important: Coding skills and experience in C++ are essential. Homework assignments involve substantial coding, partly based on a C++ finite element library. The written examination will be computer based and will comprise coding tasks. | |||||

401-3052-10L | Graph Theory | W | 10 KP | 4V + 1U | B. Sudakov | |

Kurzbeschreibung | Basics, trees, Caley's formula, matrix tree theorem, connectivity, theorems of Mader and Menger, Eulerian graphs, Hamilton cycles, theorems of Dirac, Ore, Erdös-Chvatal, matchings, theorems of Hall, König, Tutte, planar graphs, Euler's formula, Kuratowski's theorem, graph colorings, Brooks' theorem, 5-colorings of planar graphs, list colorings, Vizing's theorem, Ramsey theory, Turán's theorem | |||||

Lernziel | The students will get an overview over the most fundamental questions concerning graph theory. We expect them to understand the proof techniques and to use them autonomously on related problems. | |||||

Skript | Lecture will be only at the blackboard. | |||||

Literatur | West, D.: "Introduction to Graph Theory" Diestel, R.: "Graph Theory" Further literature links will be provided in the lecture. | |||||

Voraussetzungen / Besonderes | Students are expected to have a mathematical background and should be able to write rigorous proofs. | |||||

401-3602-00L | Applied Stochastic Processes | W | 8 KP | 3V + 1U | V. Tassion | |

Kurzbeschreibung | Poisson-Prozesse; Erneuerungsprozesse; Markovketten in diskreter und in stetiger Zeit; einige Beispiele und Anwendungen. | |||||

Lernziel | Stochastische Prozesse dienen zur Beschreibung der Entwicklung von Systemen, die sich in einer zufälligen Weise entwickeln. In dieser Vorlesung bezieht sich die Entwicklung auf einen skalaren Parameter, der als Zeit interpretiert wird, so dass wir die zeitliche Entwicklung des Systems studieren. Die Vorlesung präsentiert mehrere Klassen von stochastischen Prozessen, untersucht ihre Eigenschaften und ihr Verhalten und zeigt anhand von einigen Beispielen, wie diese Prozesse eingesetzt werden können. Die Hauptbetonung liegt auf der Theorie; "applied" ist also im Sinne von "applicable" zu verstehen. | |||||

Literatur | R. N. Bhattacharya and E. C. Waymire, "Stochastic Processes with Applications", SIAM (2009), available online: http://epubs.siam.org/doi/book/10.1137/1.9780898718997 R. Durrett, "Essentials of Stochastic Processes", Springer (2012), available online: http://link.springer.com/book/10.1007/978-1-4614-3615-7/page/1 M. Lefebvre, "Applied Stochastic Processes", Springer (2007), available online: http://link.springer.com/book/10.1007/978-0-387-48976-6/page/1 S. I. Resnick, "Adventures in Stochastic Processes", Birkhäuser (2005) | |||||

Voraussetzungen / Besonderes | Prerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L). | |||||

401-4632-15L | Causality | W | 4 KP | 2G | C. Heinze-Deml | |

Kurzbeschreibung | In statistics, we are used to search for the best predictors of some random variable. In many situations, however, we are interested in predicting a system's behavior under manipulations. For such an analysis, we require knowledge about the underlying causal structure of the system. In this course, we study concepts and theory behind causal inference. | |||||

Lernziel | After this course, you should be able to - understand the language and concepts of causal inference - know the assumptions under which one can infer causal relations from observational and/or interventional data - describe and apply different methods for causal structure learning - given data and a causal structure, derive causal effects and predictions of interventional experiments | |||||

Voraussetzungen / Besonderes | Prerequisites: basic knowledge of probability theory and regression | |||||

401-4656-21L | Deep Learning in Scientific Computing Aimed at students in a Master's Programme in Mathematics, Engineering and Physics. | W | 6 KP | 2V + 1U | S. Mishra | |

Kurzbeschreibung | Machine Learning, particularly deep learning is being increasingly applied to perform, enhance and accelerate computer simulations of models in science and engineering. This course aims to present a highly topical selection of themes in the general area of deep learning in scientific computing, with an emphasis on the application of deep learning algorithms for systems, modeled by PDEs. | |||||

Lernziel | The objective of this course will be to introduce students to advanced applications of deep learning in scientific computing. The focus will be on the design and implementation of algorithms as well as on the underlying theory that guarantees reliability of the algorithms. We will provide several examples of applications in science and engineering where deep learning based algorithms outperform state of the art methods. | |||||

Inhalt | A selection of the following topics will be presented in the lectures. 1. Issues with traditional methods for scientific computing such as Finite Element, Finite Volume etc, particularly for PDE models with high-dimensional state and parameter spaces. 2. Introduction to Deep Learning: Artificial Neural networks, Supervised learning, Stochastic gradient descent algorithms for training, different architectures: Convolutional Neural Networks, Recurrent Neural Networks, ResNets. 3. Theoretical Foundations: Universal approximation properties of the Neural networks, Bias-Variance decomposition, Bounds on approximation and generalization errors. 4. Supervised deep learning for solutions fields and observables of high-dimensional parametric PDEs. Use of low-discrepancy sequences and multi-level training to reduce generalization error. 5. Uncertainty Quantification for PDEs with supervised learning algorithms. 6. Deep Neural Networks as Reduced order models and prediction of solution fields. 7. Active Learning algorithms for PDE constrained optimization. 8. Recurrent Neural Networks and prediction of time series for dynamical systems. 9. Physics Informed Neural networks (PINNs) for the forward problem for PDEs. Applications to high-dimensional PDEs. 10. PINNs for inverse problems for PDEs, parameter identification, optimal control and data assimilation. All the algorithms will be illustrated on a variety of PDEs: diffusion models, Black-Scholes type PDEs from finance, wave equations, Euler and Navier-Stokes equations, hyperbolic systems of conservation laws, Dispersive PDEs among others. | |||||

Skript | Lecture notes will be provided at the end of the course. | |||||

Literatur | All the material in the course is based on research articles written in last 1-2 years. The relevant references will be provided. | |||||

Voraussetzungen / Besonderes | The students should be familiar with numerical methods for PDEs, for instance in courses such as Numerical Methods for PDEs for CSE, Numerical analysis of Elliptic and Parabolic PDEs, Numerical methods for hyperbolic PDEs, Computational methods for Engineering Applications. Some familiarity with basic concepts in machine learning will be beneficial. The exercises in the course rely on standard machine learning frameworks such as KERAS, TENSORFLOW or PYTORCH. So, competence in Python is helpful. | |||||

401-4944-20L | Mathematics of Data ScienceFindet dieses Semester nicht statt. | W | 8 KP | 4G | A. Bandeira | |

Kurzbeschreibung | Mostly self-contained, but fast-paced, introductory masters level course on various theoretical aspects of algorithms that aim to extract information from data. | |||||

Lernziel | Introduction to various mathematical aspects of Data Science. | |||||

Inhalt | These topics lie in overlaps of (Applied) Mathematics with: Computer Science, Electrical Engineering, Statistics, and/or Operations Research. Each lecture will feature a couple of Mathematical Open Problem(s) related to Data Science. The main mathematical tools used will be Probability and Linear Algebra, and a basic familiarity with these subjects is required. There will also be some (although knowledge of these tools is not assumed) Graph Theory, Representation Theory, Applied Harmonic Analysis, among others. The topics treated will include Dimension reduction, Manifold learning, Sparse recovery, Random Matrices, Approximation Algorithms, Community detection in graphs, and several others. | |||||

Skript | https://people.math.ethz.ch/~abandeira/BandeiraSingerStrohmer-MDS-draft.pdf | |||||

Voraussetzungen / Besonderes | The main mathematical tools used will be Probability, Linear Algebra (and real analysis), and a working knowledge of these subjects is required. In addition to these prerequisites, this class requires a certain degree of mathematical maturity--including abstract thinking and the ability to understand and write proofs. We encourage students who are interested in mathematical data science to take both this course and ``227-0434-10L Mathematics of Information'' taught by Prof. H. Bölcskei. The two courses are designed to be complementary. A. Bandeira and H. Bölcskei | |||||

401-6102-00L | Multivariate StatisticsFindet dieses Semester nicht statt. | W | 4 KP | 2G | keine Angaben | |

Kurzbeschreibung | Multivariate Statistics deals with joint distributions of several random variables. This course introduces the basic concepts and provides an overview over classical and modern methods of multivariate statistics. We will consider the theory behind the methods as well as their applications. | |||||

Lernziel | After the course, you should be able to: - describe the various methods and the concepts and theory behind them - identify adequate methods for a given statistical problem - use the statistical software "R" to efficiently apply these methods - interpret the output of these methods | |||||

Inhalt | Visualization / Principal component analysis / Multidimensional scaling / The multivariate Normal distribution / Factor analysis / Supervised learning / Cluster analysis | |||||

Skript | None | |||||

Literatur | The course will be based on class notes and books that are available electronically via the ETH library. | |||||

Voraussetzungen / Besonderes | Target audience: This course is the more theoretical version of "Applied Multivariate Statistics" (401-0102-00L) and is targeted at students with a math background. Prerequisite: A basic course in probability and statistics. Note: The courses 401-0102-00L and 401-6102-00L are mutually exclusive. You may register for at most one of these two course units. | |||||

402-0448-01L | Quantum Information Processing I: ConceptsDieser theoretisch ausgerichtete Teil QIP I bildet zusammen mit dem experimentell ausgerichteten Teil 402-0448-02L QIP II, die beide im Frühjahrssemester angeboten werden, im Master-Studiengang Physik das experimentelle Kernfach "Quantum Information Processing" mit total 10 ECTS-Kreditpunkten. | W | 5 KP | 2V + 1U | P. Kammerlander | |

Kurzbeschreibung | The course will cover the key concepts and ideas of quantum information processing, including descriptions of quantum algorithms which give the quantum computer the power to compute problems outside the reach of any classical supercomputer. Key concepts such as quantum error correction will be described. These ideas provide fundamental insights into the nature of quantum states and measurement. | |||||

Lernziel | By the end of the course students are able to explain the basic mathematical formalism of quantum mechanics and apply them to quantum information processing problems. They are able to adapt and apply these concepts and methods to analyse and discuss quantum algorithms and other quantum information-processing protocols. | |||||

Inhalt | The topics covered in the course will include quantum circuits, gate decomposition and universal sets of gates, efficiency of quantum circuits, quantum algorithms (Shor, Grover, Deutsch-Josza,..), error correction, fault-tolerant design, entanglement, teleportation and dense conding, teleportation of gates, and cryptography. | |||||

Skript | More details to follow. | |||||

Literatur | Quantum Computation and Quantum Information Michael Nielsen and Isaac Chuang Cambridge University Press | |||||

Voraussetzungen / Besonderes | A good understanding of linear algebra is recommended. | |||||

701-0104-00L | Statistical Modelling of Spatial Data | W | 3 KP | 2G | A. J. Papritz | |

Kurzbeschreibung | In environmental sciences one often deals with spatial data. When analysing such data the focus is either on exploring their structure (dependence on explanatory variables, autocorrelation) and/or on spatial prediction. The course provides an introduction to geostatistical methods that are useful for such analyses. | |||||

Lernziel | The course will provide an overview of the basic concepts and stochastic models that are used to model spatial data. In addition, participants will learn a number of geostatistical techniques and acquire familiarity with R software that is useful for analyzing spatial data. | |||||

Inhalt | After an introductory discussion of the types of problems and the kind of data that arise in environmental research, an introduction into linear geostatistics (models: stationary and intrinsic random processes, modelling large-scale spatial patterns by linear regression, modelling autocorrelation by variogram; kriging: mean square prediction of spatial data) will be taught. The lectures will be complemented by data analyses that the participants have to do themselves. | |||||

Skript | Slides, descriptions of the problems for the data analyses and solutions to them will be provided. | |||||

Literatur | P.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer. | |||||

Voraussetzungen / Besonderes | Familiarity with linear regression analysis (e.g. equivalent to the first part of the course 401-0649-00L Applied Statistical Regression) and with the software R (e.g. 401-6215-00L Using R for Data Analysis and Graphics (Part I), 401-6217-00L Using R for Data Analysis and Graphics (Part II)) are required for attending the course. |

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