# Search result: Catalogue data in Spring Semester 2018

Data Science Master | ||||||

Core Courses | ||||||

Data Analysis | ||||||

Information and Learning | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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227-0434-10L | Mathematics of Information | W | 8 credits | 3V + 2U + 2A | H. Bölcskei | |

Abstract | The class focuses on fundamental mathematical aspects of data sciences: Information theory (lossless and lossy compression), sampling theory, compressed sensing, dimensionality reduction (Johnson-Lindenstrauss Lemma), randomized algorithms for large-scale numerical linear algebra, approximation theory, neural networks as function approximators, mathematical foundations of deep learning. | |||||

Objective | After attending this lecture, participating in the exercise sessions, and working on the homework problem sets, students will have acquired a working knowledge of the most commonly used mathematical theories in data science. Students will also have to carry out a research project, either individually or in groups, with presentations at the end of the semester. | |||||

Content | 1. Information theory: Entropy, mutual information, lossy compression, rate-distortion theory, lossless compression, arithmetic coding, Lempel-Ziv compression 2. Signal representations: Frames in finite-dimensional spaces, frames in Hilbert spaces, wavelets, Gabor expansions 3. Sampling theorems: The sampling theorem as a frame expansion, irregular sampling, multi-band sampling, density theorems, spectrum-blind sampling 4. Sparsity and compressed sensing: Uncertainty principles, recovery algorithms, Lasso, matching pursuits, compressed sensing, non-linear approximation, best k-term approximation, super-resolution 5. High-dimensional data and dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma, sketching 6. Randomized algorithms for large-scale numerical linear algebra: Large-scale matrix computations, randomized algorithms for approximate matrix factorizations, matrix sketching, fast algorithms for large-scale FFTs 7. Mathematics of (deep) neural networks: Universal function approximation with single-and multi-layer networks, fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, geometry of decision surfaces, convolutional neural networks, scattering networks | |||||

Lecture notes | Detailed lecture notes will be provided as we go along. | |||||

Prerequisites / Notice | This course is aimed at students with a background in basic linear algebra, analysis, and probability. We will, however, review required mathematical basics throughout the semester in the exercise sessions. | |||||

Statistics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3632-00L | Computational Statistics | W | 10 credits | 3V + 2U | M. H. Maathuis | |

Abstract | Computational Statistics deals with modern statistical methods of data analysis (aka "data science") for prediction and inference. The course provides an overview of existing methods. The course is hands-on, and methods are applied using the statistical programming language R. | |||||

Objective | In this class, 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. | |||||

Content | See the class website | |||||

Prerequisites / Notice | At least one semester of (basic) probability and statistics. Programming experience is helpful but not required. | |||||

Data Management | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

261-5110-00L | Optimization for Data Science | W | 8 credits | 3V + 2U + 2A | B. Gärtner, D. Steurer | |

Abstract | This course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science. | |||||

Objective | Understanding the theoretical and practical aspects of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science. | |||||

Content | This course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science. In the first part of the course, we will discuss how classical first and second order methods such as gradient descent and Newton's method can be adapated to scale to large datasets, in theory and in practice. We also cover some new algorithms and paradigms that have been developed specifically in the context of data science. The emphasis is not so much on the application of these methods (many of which are covered in other courses), but on understanding and analyzing the methods themselves. 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. | |||||

Prerequisites / Notice | 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. | |||||

Core Electives | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

151-0566-00L | Recursive Estimation | W | 4 credits | 2V + 1U | R. D'Andrea | |

Abstract | Estimation of the state of a dynamic system based on a model and observations in a computationally efficient way. | |||||

Objective | Learn the basic recursive estimation methods and their underlying principles. | |||||

Content | Introduction to state estimation; probability review; Bayes' theorem; Bayesian tracking; extracting estimates from probability distributions; Kalman filter; extended Kalman filter; particle filter; observer-based control and the separation principle. | |||||

Lecture notes | Lecture notes available on course website: http://www.idsc.ethz.ch/education/lectures/recursive-estimation.html | |||||

Prerequisites / Notice | Requirements: Introductory probability theory and matrix-vector algebra. | |||||

227-0150-00L | Energy-Efficient Parallel Computing Systems for Data Analytics Previously called "Advanced System-on-chip Design: Integrated Parallel Computing Architectures" | W | 6 credits | 4G | L. Benini | |

Abstract | Advanced Parallel Computing Architectures and related design issues. It will cover multi-cores, many-cores, vector engines, GP-GPUs, application-specific processors and heterogeneous compute accelerators. Focus on integrated architectures for data analytics applications. Special emphasis given to energy-efficiency issues and hardware-software design for power and energy minimizazion. | |||||

Objective | Give in-depth understanding of the links and dependencies between architectures and their energy-efficient implementation and to get a comprehensive exposure to state-of-the-art computing platforma for data anlytics applications. Practical experience will also be gained through practical exercises and mini-projects (hardware and software) assigned on specific topics. | |||||

Content | The course will cover advanced parallel computing architectures architectures, with an in-depth view on design challenges related to advanced silicon technology and state-of-the-art system integration options (nanometer silicon technology, novel storage devices, three-dimensional integration, advanced system packaging). The emphasis will be on programmable parallel architectures, namely, multi and many- cores, GPUs, vector accelerators, application-specific processors, heterogeneous platforms, and the complex design choices required to achieve scalability and energy proportionality. The course will will also delve into system design, touching on hardware-software tradeoffs and full-system analysis and optimization taking into account non-functional constraints and quality metrics, such as power consumption, thermal dissipation, reliability and variability. The application focus will be on emerging data analytics both in the cloud at at the edges (near-sensor analytics). | |||||

Lecture notes | Slides will be provided to accompany lectures. Pointers to scientific literature will be given. Exercise scripts and tutorials will be provided. | |||||

Literature | D. Patterson, J. Hennessy, Computer Architecture, Fifth Edition: A Quantitative Approach (The Morgan Kaufmann Series in Computer Architecture and Design), 2011. D. Patterson, J. Hennessy, Computer Organization and Design, Fifth Edition: The Hardware/Software Interface (The Morgan Kaufmann Series in Computer Architecture and Design), 2013. | |||||

Prerequisites / Notice | Knowledge of digital design at the level of "Design of Digital Circuits SS12" is required. Knowledge of basic VLSI design at the level of "VLSI I: Architectures of VLSI Circuits" is required | |||||

227-0224-00L | Stochastic Systems | W | 4 credits | 2V + 1U | F. Herzog | |

Abstract | Probability. Stochastic processes. Stochastic differential equations. Ito. Kalman filters. St Stochastic optimal control. Applications in financial engineering. | |||||

Objective | Stochastic dynamic systems. Optimal control and filtering of stochastic systems. Examples in technology and finance. | |||||

Content | - Stochastic processes - Stochastic calculus (Ito) - Stochastic differential equations - Discrete time stochastic difference equations - Stochastic processes AR, MA, ARMA, ARMAX, GARCH - Kalman filter - Stochastic optimal control - Applications in finance and engineering | |||||

Lecture notes | H. P. Geering et al., Stochastic Systems, Measurement and Control Laboratory, 2007 and handouts | |||||

227-0420-00L | Information Theory II Does not take place this semester. | W | 6 credits | 2V + 2U | A. Lapidoth | |

Abstract | This course builds on Information Theory I. It introduces additional topics in single-user communication, connections between Information Theory and Statistics, and Network Information Theory. | |||||

Objective | The course has two objectives: to introduce the students to the key information theoretic results that underlay the design of communication systems and to equip the students with the tools that are needed to conduct research in Information Theory. | |||||

Content | Differential entropy, maximum entropy, the Gaussian channel and water filling, the entropy-power inequality, Sanov's Theorem, Fisher information, the broadcast channel, the multiple-access channel, Slepian-Wolf coding, and the Gelfand-Pinsker problem. | |||||

Lecture notes | n/a | |||||

Literature | T.M. Cover and J.A. Thomas, Elements of Information Theory, second edition, Wiley 2006 | |||||

227-0558-00L | Principles of Distributed Computing | W | 6 credits | 2V + 2U + 1A | R. Wattenhofer, M. Ghaffari | |

Abstract | We study the fundamental issues underlying the design of distributed systems: communication, coordination, fault-tolerance, locality, parallelism, self-organization, symmetry breaking, synchronization, uncertainty. We explore essential algorithmic ideas and lower bound techniques. | |||||

Objective | Distributed computing is essential in modern computing and communications systems. Examples are on the one hand large-scale networks such as the Internet, and on the other hand multiprocessors such as your new multi-core laptop. This course introduces the principles of distributed computing, emphasizing the fundamental issues underlying the design of distributed systems and networks: communication, coordination, fault-tolerance, locality, parallelism, self-organization, symmetry breaking, synchronization, uncertainty. We explore essential algorithmic ideas and lower bound techniques, basically the "pearls" of distributed computing. We will cover a fresh topic every week. | |||||

Content | Distributed computing models and paradigms, e.g. message passing, shared memory, synchronous vs. asynchronous systems, time and message complexity, peer-to-peer systems, small-world networks, social networks, sorting networks, wireless communication, and self-organizing systems. Distributed algorithms, e.g. leader election, coloring, covering, packing, decomposition, spanning trees, mutual exclusion, store and collect, arrow, ivy, synchronizers, diameter, all-pairs-shortest-path, wake-up, and lower bounds | |||||

Lecture notes | Available. Our course script is used at dozens of other universities around the world. | |||||

Literature | Lecture Notes By Roger Wattenhofer. These lecture notes are taught at about a dozen different universities through the world. Distributed Computing: Fundamentals, Simulations and Advanced Topics Hagit Attiya, Jennifer Welch. McGraw-Hill Publishing, 1998, ISBN 0-07-709352 6 Introduction to Algorithms Thomas Cormen, Charles Leiserson, Ronald Rivest. The MIT Press, 1998, ISBN 0-262-53091-0 oder 0-262-03141-8 Disseminatin of Information in Communication Networks Juraj Hromkovic, Ralf Klasing, Andrzej Pelc, Peter Ruzicka, Walter Unger. Springer-Verlag, Berlin Heidelberg, 2005, ISBN 3-540-00846-2 Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes Frank Thomson Leighton. Morgan Kaufmann Publishers Inc., San Francisco, CA, 1991, ISBN 1-55860-117-1 Distributed Computing: A Locality-Sensitive Approach David Peleg. Society for Industrial and Applied Mathematics (SIAM), 2000, ISBN 0-89871-464-8 | |||||

Prerequisites / Notice | Course pre-requisites: Interest in algorithmic problems. (No particular course needed.) | |||||

252-0211-00L | Information Security | W | 8 credits | 4V + 3U | D. Basin, S. Capkun | |

Abstract | This course provides an introduction to Information Security. The focus is on fundamental concepts and models, basic cryptography, protocols and system security, and privacy and data protection. While the emphasis is on foundations, case studies will be given that examine different realizations of these ideas in practice. | |||||

Objective | Master fundamental concepts in Information Security and their application to system building. (See objectives listed below for more details). | |||||

Content | 1. Introduction and Motivation (OBJECTIVE: Broad conceptual overview of information security) Motivation: implications of IT on society/economy, Classical security problems, Approaches to defining security and security goals, Abstractions, assumptions, and trust, Risk management and the human factor, Course verview. 2. Foundations of Cryptography (OBJECTIVE: Understand basic cryptographic mechanisms and applications) Introduction, Basic concepts in cryptography: Overview, Types of Security, computational hardness, Abstraction of channel security properties, Symmetric encryption, Hash functions, Message authentication codes, Public-key distribution, Public-key cryptosystems, Digital signatures, Application case studies, Comparison of encryption at different layers, VPN, SSL, Digital payment systems, blind signatures, e-cash, Time stamping 3. Key Management and Public-key Infrastructures (OBJECTIVE: Understand the basic mechanisms relevant in an Internet context) Key management in distributed systems, Exact characterization of requirements, the role of trust, Public-key Certificates, Public-key Infrastructures, Digital evidence and non-repudiation, Application case studies, Kerberos, X.509, PGP. 4. Security Protocols (OBJECTIVE: Understand network-oriented security, i.e.. how to employ building blocks to secure applications in (open) networks) Introduction, Requirements/properties, Establishing shared secrets, Principal and message origin authentication, Environmental assumptions, Dolev-Yao intruder model and variants, Illustrative examples, Formal models and reasoning, Trace-based interleaving semantics, Inductive verification, or model-checking for falsification, Techniques for protocol design, Application case study 1: from Needham-Schroeder Shared-Key to Kerberos, Application case study 2: from DH to IKE. 5. Access Control and Security Policies (OBJECTIVES: Study system-oriented security, i.e., policies, models, and mechanisms) Motivation (relationship to CIA, relationship to Crypto) and examples Concepts: policies versus models versus mechanisms, DAC and MAC, Modeling formalism, Access Control Matrix Model, Roll Based Access Control, Bell-LaPadula, Harrison-Ruzzo-Ullmann, Information flow, Chinese Wall, Biba, Clark-Wilson, System mechanisms: Operating Systems, Hardware Security Features, Reference Monitors, File-system protection, Application case studies 6. Anonymity and Privacy (OBJECTIVE: examine protection goals beyond standard CIA and corresponding mechanisms) Motivation and Definitions, Privacy, policies and policy languages, mechanisms, problems, Anonymity: simple mechanisms (pseudonyms, proxies), Application case studies: mix networks and crowds. 7. Larger application case study: GSM, mobility | |||||

252-0526-00L | Statistical Learning Theory | W | 6 credits | 2V + 3P | J. M. Buhmann | |

Abstract | The course covers advanced methods of statistical learning : Statistical learning theory;variational methods and optimization, e.g., maximum entropy techniques, information bottleneck, deterministic and simulated annealing; clustering for vectorial, histogram and relational data; model selection; graphical models. | |||||

Objective | The course surveys recent methods of statistical learning. The fundamentals of machine learning as presented in the course "Introduction to Machine Learning" are expanded and in particular, the theory of statistical learning is discussed. | |||||

Content | # Theory of estimators: How can we measure the quality of a statistical estimator? We already discussed bias and variance of estimators very briefly, but the interesting part is yet to come. # Variational methods and optimization: We consider optimization approaches for problems where the optimizer is a probability distribution. Concepts we will discuss in this context include: * Maximum Entropy * Information Bottleneck * Deterministic Annealing # Clustering: The problem of sorting data into groups without using training samples. This requires a definition of ``similarity'' between data points and adequate optimization procedures. # Model selection: We have already discussed how to fit a model to a data set in ML I, which usually involved adjusting model parameters for a given type of model. Model selection refers to the question of how complex the chosen model should be. As we already know, simple and complex models both have advantages and drawbacks alike. # Statistical physics models: approaches for large systems approximate optimization, which originate in the statistical physics (free energy minimization applied to spin glasses and other models); sampling methods based on these models | |||||

Lecture notes | A draft of a script will be provided; transparencies of the lectures will be made available. | |||||

Literature | Hastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer, 2001. L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern recognition. Springer, New York, 1996 | |||||

Prerequisites / Notice | Requirements: knowledge of the Machine Learning course basic knowledge of statistics, interest in statistical methods. It is recommended that Introduction to Machine Learning (ML I) is taken first; but with a little extra effort Statistical Learning Theory can be followed without the introductory course. | |||||

252-0538-00L | Shape Modeling and Geometry Processing | W | 5 credits | 2V + 1U + 1A | S. Coros | |

Abstract | This course covers some of the latest developments in geometric modeling and digital geometry processing. Topics include surface modeling based on polygonal meshes, mesh generation, surface reconstruction, mesh fairing and simplification, discrete differential geometry, interactive shape editing, topics in digital shape fabrication. | |||||

Objective | The students will learn how to design, program and analyze algorithms and systems for interactive 3D shape modeling and digital geometry processing. | |||||

Content | Recent advances in 3D digital geometry processing have created a plenitude of novel concepts for the mathematical representation and interactive manipulation of geometric models. This course covers some of the latest developments in geometric modeling and digital geometry processing. Topics include surface modeling based on triangle meshes, mesh generation, surface reconstruction, mesh fairing and simplification, discrete differential geometry, interactive shape editing and digital shape fabrication. | |||||

Lecture notes | Slides and course notes | |||||

Prerequisites / Notice | Prerequisites: Visual Computing, Computer Graphics or an equivalent class. Experience with C++ programming. Some background in geometry or computational geometry is helpful, but not necessary. | |||||

252-0579-00L | 3D Vision | W | 4 credits | 3G | T. Sattler, M. R. Oswald | |

Abstract | The course covers camera models and calibration, feature tracking and matching, camera motion estimation via simultaneous localization and mapping (SLAM) and visual odometry (VO), epipolar and mult-view geometry, structure-from-motion, (multi-view) stereo, augmented reality, and image-based (re-)localization. | |||||

Objective | After attending this course, students will: 1. understand the core concepts for recovering 3D shape of objects and scenes from images and video. 2. be able to implement basic systems for vision-based robotics and simple virtual/augmented reality applications. 3. have a good overview over the current state-of-the art in 3D vision. 4. be able to critically analyze and asses current research in this area. | |||||

Content | The goal of this course is to teach the core techniques required for robotic and augmented reality applications: How to determine the motion of a camera and how to estimate the absolute position and orientation of a camera in the real world. This course will introduce the basic concepts of 3D Vision in the form of short lectures, followed by student presentations discussing the current state-of-the-art. The main focus of this course are student projects on 3D Vision topics, with an emphasis on robotic vision and virtual and augmented reality applications. | |||||

252-3005-00L | Natural Language Understanding | W | 4 credits | 2V + 1U | T. Hofmann, M. Ciaramita | |

Abstract | This course presents topics in natural language processing with an emphasis on modern techniques, primarily focusing on statistical and deep learning approaches. The course provides an overview of the primary areas of research in language processing as well as a detailed exploration of the models and techniques used both in research and in commercial natural language systems. | |||||

Objective | The objective of the course is to learn the basic concepts in the statistical processing of natural languages. The course will be project-oriented so that the students can also gain hands-on experience with state-of-the-art tools and techniques. | |||||

Content | This course presents an introduction to general topics and techniques used in natural language processing today, primarily focusing on statistical approaches. The course provides an overview of the primary areas of research in language processing as well as a detailed exploration of the models and techniques used both in research and in commercial natural language systems. | |||||

Literature | Lectures will make use of textbooks such as the one by Jurafsky and Martin where appropriate, but will also make use of original research and survey papers. | |||||

261-5130-00L | Research in Data Science | W | 6 credits | 13A | Professors | |

Abstract | Independent work under the supervision of a core data science professor. | |||||

Objective | Independent work under the supervision of a core data science professor. An approval of the director of studies is required for a non-core DS professor. | |||||

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

Prerequisites / Notice | 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. | |||||

263-0008-00L | Computational Intelligence LabOnly for master students, otherwise a special permission by the study administration of D-INFK is required. | W | 8 credits | 2V + 2U + 1A | T. Hofmann | |

Abstract | 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. | |||||

Objective | 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 two to three 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.) | |||||

Content | see course description | |||||

263-2925-00L | Program Analysis for System Security and Reliability | W | 5 credits | 2V + 1U + 1A | M. Vechev | |

Abstract | The course introduces modern analysis and synthesis techniques (both, deterministic and probabilistic) and shows how to apply these methods to build reliable and secure systems spanning the domains of blockchain, computer networks and deep learning. | |||||

Objective | * Understand how classic analysis and synthesis techniques work, including discrete and probabilistic methods. * Understand how to apply the methods to generate attacks and create defenses against applications in blockchain, computer networks and deep learning. * Understand the state-of-the-art in the area as well as future trends. | |||||

Content | The course will illustrate how the methods can be used to create more secure and reliable systems across four application domains: Part I: Analysis and Synthesis for Computer Networks: 1. Analysis: Datalog, Batfish 2. Synthesis: CEGIS, SyNET (http://synet.ethz.ch) 3. Probabilistic: (PSI: http://psisolver.org), its applications to networks (Bayonet) Part II: Blockchain security 1. Introduction to space and tools. 2. Automated symbolic reasoning. 3. Applications: verification of smart contracts (http://www.securify.ch) Part III: Security and Robustness of Deep Learning: 1. Basics: affine transforms, activation functions 2. Attacks: gradient based method to adversarial generation 3. Defenses: affine domains, AI2 (http://ai2.ethz.ch) Part IV: Probabilistic Security: 1. Enforcement: PSI + Spire. 2. Graphical models: CRFs, Structured SVM, Pseudo-likelihood. 3. Practical statistical de-obfuscation: DeGuard: http://apk-deguard.com, JSNice: http://jsnice.org, and more. To gain a deeper understanding, the course will involve a hands-on programming project. | |||||

263-3710-00L | Machine Perception Students, who have already taken 263-3700-00 User Interface Engineering are not allowed to register for this course! | W | 5 credits | 2V + 1U + 1A | O. Hilliges | |

Abstract | Recent developments in neural network (aka “deep learning”) have drastically advanced the performance of machine perception systems in a variety of areas including drones, self-driving cars and intelligent UIs. This course is a deep dive into details of the deep learning algorithms and architectures for a variety of perceptual tasks. | |||||

Objective | 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 motion. 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. | |||||

Content | We will focus on teaching how to set up the problem of machine perception, the learning algorithms (e.g. backpropagation), practical engineering aspects as well as advanced deep learning algorithms including generative models. The course covers the following main areas: I) Machine-learning algorithms for input recognition, computer vision and image classification (human pose, object detection, gestures, etc.) II) Deep-learning models for the analysis of time-series data (temporal sequences of motion) III) Learning of generative models for synthesis and prediction of human activity. Specific topics include: • Deep learning basics: ○ Neural Networks and training (i.e., backpropagation) ○ Feedforward Networks ○ Recurrent Neural Networks • Deep Learning techniques user input recognition: ○ Convolutional Neural Networks for classification ○ Fully Convolutional architectures for dense per-pixel tasks (i.e., segmentation) ○ LSTMs & related for time series analysis ○ Generative Models (GANs, Variational Autoencoders) • Case studies from research in computer vision, HCI, robotics and signal processing | |||||

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

Prerequisites / Notice | 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 is not meant as extensive tutorial of how to train deep networks with Tensorflow.. Please take note of the following conditions: 1) The number of participants is limited to 100 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 TensorFlow, scikit-learn and scikit-image. We will provide introductions to TensorFlow and other libraries that are needed but will not provide introductions to basic programming or Python. The following courses are strongly recommended as prerequisite: * "Machine Learning" * "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. | |||||

401-0674-00L | Numerical Methods for Partial Differential EquationsNot meant for BSc/MSc students of mathematics. | W | 8 credits | 4V + 2U + 1A | R. Hiptmair | |

Abstract | 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. | |||||

Objective | Main skills to be acquired in this course: * Ability to implement advanced 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. | |||||

Content | 1 Case Study: A Two-point Boundary Value Problem 1.1 Introduction 1.2 A model problem 1.3 Variational approach 1.4 Simplified model 1.5 Discretization 1.5.1 Galerkin discretization 1.5.2 Collocation [optional] 1.5.3 Finite differences 1.6 Convergence 2 Second-order Scalar Elliptic Boundary Value Problems 2.1 Equilibrium models 2.1.1 Taut membrane 2.1.2 Electrostatic fields 2.1.3 Quadratic minimization problems 2.2 Sobolev spaces 2.3 Variational formulations 2.4 Equilibrium models: Boundary value problems 3 Finite Element Methods (FEM) 3.1 Galerkin discretization 3.2 Case study: Triangular linear FEM in two dimensions 3.3 Building blocks of general FEM 3.4 Lagrangian FEM 3.4.1 Simplicial Lagrangian FEM 3.4.2 Tensor-product Lagrangian FEM 3.5 Implementation of FEM in C++ 3.5.1 Mesh file format (Gmsh) 3.5.2 Mesh data structures (DUNE) 3.5.3 Assembly 3.5.4 Local computations and quadrature 3.5.5 Incorporation of essential boundary conditions 3.6 Parametric finite elements 3.6.1 Affine equivalence 3.6.2 Example: Quadrilaterial Lagrangian finite elements 3.6.3 Transformation techniques 3.6.4 Boundary approximation 3.7 Linearization [optional] 4 Finite Differences (FD) and Finite Volume Methods (FV) [optional] 4.1 Finite differences 4.2 Finite volume methods (FVM) 5 Convergence and Accuracy 5.1 Galerkin error estimates 5.2 Empirical Convergence of FEM 5.3 Finite element error estimates 5.4 Elliptic regularity theory 5.5 Variational crimes 5.6 Duality techniques [optional] 5.7 Discrete maximum principle [optional] 6 2nd-Order Linear Evolution Problems 6.1 Parabolic initial-boundary value problems 6.1.1 Heat equation 6.1.2 Spatial variational formulation 6.1.3 Method of lines 6.1.4 Timestepping 6.1.5 Convergence 6.2 Wave equations [optional] 6.2.1 Vibrating membrane 6.2.2 Wave propagation 6.2.3 Method of lines 6.2.4 Timestepping 6.2.5 CFL-condition 7 Convection-Diffusion Problems 7.1 Heat conduction in a fluid 7.1.1 Modelling fluid flow 7.1.2 Heat convection and diffusion 7.1.3 Incompressible fluids 7.1.4 Transient heat conduction 7.2 Stationary convection-diffusion problems 7.2.1 Singular perturbation 7.2.2 Upwinding 7.3 Transient convection-diffusion BVP 7.3.1 Method of lines 7.3.2 Transport equation 7.3.3 Lagrangian split-step method 7.3.4 Semi-Lagrangian method 8 Numerical Methods for Conservation Laws 8.1 Conservation laws: Examples 8.2 Scalar conservation laws in 1D 8.3 Conservative finite volume discretization 8.3.1 Semi-discrete conservation form 8.3.2 Discrete conservation property 8.3.3 Numerical flux functions 8.3.4 Montone schemes 8.4 Timestepping 8.4.1 Linear stability 8.4.2 CFL-condition 8.4.3 Convergence 8.5 Higher order conservative schemes [optional] 8.5.1 Slope limiting 8.5.2 MUSCL scheme 8.6. FV-schemes for systems of conservation laws [optional] | |||||

Lecture notes | Lecture documents and classroom notes will be made available to the audience as PDF. | |||||

Literature | 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. | |||||

Prerequisites / Notice | 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. | |||||

401-3052-05L | Graph Theory | W | 5 credits | 2V + 1U | B. Sudakov | |

Abstract | Basic notions, trees, spanning trees, Caley's formula, vertex and edge connectivity, blocks, 2-connectivity, Mader's theorem, Menger's theorem, Eulerian graphs, Hamilton cycles, Dirac's theorem, matchings, theorems of Hall, König and Tutte, planar graphs, Euler's formula, basic non-planar graphs, graph colorings, greedy colorings, Brooks' theorem, 5-colorings of planar graphs | |||||

Objective | 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. | |||||

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

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

Prerequisites / Notice | NOTICE: This course unit was previously offered as 252-1408-00L Graphs and Algorithms. | |||||

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

Abstract | 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 | |||||

Objective | 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. | |||||

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

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

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