Suchergebnis: Katalogdaten im Frühjahrssemester 2020

Statistik Master Information
Die hier aufgelisteten Lehrveranstaltungen gehören zum Curriculum des Master-Studiengangs Statistik. Die entsprechenden KP gelten nicht als Mobilitäts-KP, auch wenn gewisse Lerneinheiten nicht an der ETH Zürich belegt werden können.
Vertiefungs- und Wahlfächer
Statistische und mathematische Fächer
NummerTitelTypECTSUmfangDozierende
401-4632-15LCausality Information W4 KP2GC. Heinze-Deml
KurzbeschreibungIn 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.
LernzielAfter 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 / BesonderesPrerequisites: basic knowledge of probability theory and regression
401-4627-00LEmpirical Process Theory and ApplicationsW4 KP2VS. van de Geer
KurzbeschreibungEmpirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc.
Lernziel
InhaltIn this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection.
401-3632-00LComputational StatisticsW8 KP3V + 1UM. H. Maathuis
KurzbeschreibungWe discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R.
LernzielThe 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.
Voraussetzungen / BesonderesAt least one semester of (basic) probability and statistics.

Programming experience is helpful but not required.
401-3602-00LApplied Stochastic Processes Information
Findet dieses Semester nicht statt.
W8 KP3V + 1Ukeine Angaben
KurzbeschreibungPoisson-Prozesse; Erneuerungsprozesse; Markovketten in diskreter und in stetiger Zeit; einige Beispiele und Anwendungen.
LernzielStochastische 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.
LiteraturR. N. Bhattacharya and E. C. Waymire, "Stochastic Processes with Applications", SIAM (2009), available online: Link
R. Durrett, "Essentials of Stochastic Processes", Springer (2012), available online: Link
M. Lefebvre, "Applied Stochastic Processes", Springer (2007), available online: Link
S. I. Resnick, "Adventures in Stochastic Processes", Birkhäuser (2005)
Voraussetzungen / BesonderesPrerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L).
401-3642-00LBrownian Motion and Stochastic Calculus Information W10 KP4V + 1UW. Werner
KurzbeschreibungThis course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.
LernzielThis course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.
SkriptLecture notes will be distributed in class.
Literatur- J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016).
- I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991).
- D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005).
- L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000).
- D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006).
Voraussetzungen / BesonderesFamiliarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in
- J. Jacod, P. Protter, Probability Essentials, Springer (2004).
- R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010).
401-6228-00LProgramming with R for Reproducible Research Information W1 KP1GM. Mächler
KurzbeschreibungDeeper understanding of R: Function calls, rather than "commands".
Reproducible research and data analysis via Sweave and Rmarkdown.
Limits of floating point arithmetic.
Understanding how functions work. Environments, packages, namespaces.
Closures, i.e., Functions returning functions.
Lists and [mc]lapply() for easy parallelization.
Performance measurement and improvements.
LernzielLearn to understand R as a (very versatile and flexible) programming language and learn about some of its lower level functionalities which are needed to understand *why* R works the way it does.
InhaltSee "Skript": Link
SkriptMaterial available from Github
Link

(typically will be updated during course)
LiteraturNorman Matloff (2011) The Art of R Programming - A tour of statistical software design.
no starch press, San Francisco. on stock at Polybuchhandlung (CHF 42.-).

More material, notably H.Wickam's "Advanced R" : see my ProgRRR github page.
Voraussetzungen / BesonderesR Knowledge on the same level as after *both* parts of the ETH lecture
401-6217-00L Using R for Data Analysis and Graphics
Link

An interest to dig deeper than average R users do.

Bring your own laptop with a recent version of R installed
401-3629-00LQuantitative Risk Management Information W4 KP2V + 1UP. Cheridito
KurzbeschreibungThis course introduces methods from probability theory and statistics that can be used to model financial risks. Topics addressed include loss distributions, risk measures, extreme value theory, multivariate models, copulas, dependence structures and operational risk.
LernzielThe goal is to learn the most important methods from probability theory and statistics used in financial risk modeling.
Inhalt1. Introduction
2. Basic Concepts in Risk Management
3. Empirical Properties of Financial Data
4. Financial Time Series
5. Extreme Value Theory
6. Multivariate Models
7. Copulas and Dependence
8. Operational Risk
SkriptCourse material is available on Link
LiteraturQuantitative Risk Management: Concepts, Techniques and Tools
AJ McNeil, R Frey and P Embrechts
Princeton University Press, Princeton, 2015 (Revised Edition)
Link
Voraussetzungen / BesonderesThe course corresponds to the Risk Management requirement for the SAA ("Aktuar SAV Ausbildung") as well as for the Master of Science UZH-ETH in Quantitative Finance.
401-4658-00LComputational Methods for Quantitative Finance: PDE Methods Information Belegung eingeschränkt - Details anzeigen W6 KP3V + 1UC. Schwab
KurzbeschreibungIntroduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB programming
and knowledge of numerical mathematics at ETH BSc level.
LernzielIntroduce the main methods for efficient numerical valuation of derivative contracts in a
Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility
models. Develop implementation of pricing methods in MATLAB.
Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation.
Inhalt1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic
volatility models.
2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees.
European contracts.
3. Finite Difference methods for Asian, American and Barrier type contracts.
4. Finite element methods for European and American style contracts.
5. Pricing under local and stochastic volatility in Black-Scholes Markets.
6. Finite Element Methods for option pricing under Levy processes. Treatment of
integrodifferential operators.
7. Stochastic volatility models for Levy processes.
8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and
stochastic volatility models in Black Scholes and Levy markets.
9. Introduction to sparse grid option pricing techniques.
SkriptThere will be english, typed lecture notes as well as MATLAB software for registered participants in the course.
LiteraturR. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004.

Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005.

D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008.

J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000.

N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013.
401-2284-00LMass und Integral Information W6 KP3V + 2UF. Da Lio
KurzbeschreibungAbstrakte Mass- und Integrationstheorie, inklusive: Satz von Caratheodory, Lebesgue-Mass, Konvergenzsätze, L^p-Räume, Satz von Radon-Nikodym, Produktmasse und Satz von Fubini, Masse auf topologischen Räumen
LernzielGrundlagen der abstrakten Mass- und Integrationstheorie
InhaltAbstrakte Mass- und Integrationstheorie, inklusive: Satz von Caratheodory, Lebesgue-Mass, Konvergenzsätze, L^p-Räume, Satz von Radon-Nikodym, Produktmasse und Satz von Fubini, Masse auf topologischen Räumen
SkriptNew lecture notes in English will be made available during the course
Literatur1. L. Evans and R.F. Gariepy " Measure theory and fine properties of functions"
2. Walter Rudin "Real and complex analysis"
3. R. Bartle The elements of Integration and Lebesgue Measure
4. Das Skript von Prof. Michael Struwe FS 2013, Link.
5. Das Skript von Prof. Urs Lang FS 2019, Link
6. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis: Link
.
401-3903-11LGeometric Integer ProgrammingW6 KP2V + 1UJ. Paat
KurzbeschreibungInteger programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems.
LernzielThe purpose of the lecture is to provide a geometric treatment of the theory of integer optimization.
InhaltKey topics are:

- Lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension.

- Structural properties of integer sets that reveal other parameters affecting the complexity of integer problems

- Duality theory for integer optimization problems from the vantage point of lattice free sets.
Skriptnot available, blackboard presentation
LiteraturLecture notes will be provided.

Other helpful materials include

Bertsimas, Weismantel: Optimization over Integers, 2005

and

Schrijver: Theory of linear and integer programming, 1986.
Voraussetzungen / Besonderes"Mathematical Optimization" (401-3901-00L)
401-4944-20LMathematics of Data ScienceW8 KP4GA. Bandeira
KurzbeschreibungMostly self-contained, but fast-paced, introductory masters level course on various theoretical aspects of algorithms that aim to extract information from data.
LernzielIntroduction to various mathematical aspects of Data Science.
InhaltThese 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.
SkriptLink
Voraussetzungen / BesonderesThe 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
227-0434-10LMathematics of Information Information W8 KP3V + 2U + 2AH. Bölcskei
KurzbeschreibungThe class focuses on mathematical aspects of

1. Information science: Sampling theorems, frame theory, compressed sensing, sparsity, super-resolution, spectrum-blind sampling, subspace algorithms, dimensionality reduction

2. Learning theory: Approximation theory, uniform laws of large numbers, Rademacher complexity, Vapnik-Chervonenkis dimension
LernzielThe aim of the class is to familiarize the students with the most commonly used mathematical theories in data science, high-dimensional data analysis, and learning theory. The class consists of the lecture, exercise sessions with homework problems, and of a research project, which can be carried out either individually or in groups. The research project consists of either 1. software development for the solution of a practical signal processing or machine learning problem or 2. the analysis of a research paper or 3. a theoretical research problem of suitable complexity. Students are welcome to propose their own project at the beginning of the semester. The outcomes of all projects have to be presented to the entire class at the end of the semester.
InhaltMathematics of Information

1. Signal representations: Frame theory, wavelets, Gabor expansions, sampling theorems, density theorems

2. Sparsity and compressed sensing: Sparse linear models, uncertainty relations in sparse signal recovery, matching pursuits, super-resolution, spectrum-blind sampling, subspace algorithms (MUSIC, ESPRIT, matrix pencil), estimation in the high-dimensional noisy case, Lasso

3. Dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma

Mathematics of Learning

4. Approximation theory: Nonlinear approximation theory, fundamental limits on compressibility of signal classes, Kolmogorov-Tikhomirov epsilon-entropy of signal classes, optimal compression of signal classes, recovery from incomplete data, information-based complexity, curse of dimensionality

5. Uniform laws of large numbers: Rademacher complexity, Vapnik-Chervonenkis dimension, classes with polynomial discrimination, blessings of dimensionality
SkriptDetailed lecture notes will be provided at the beginning of the semester and as we go along.
Voraussetzungen / BesonderesThis course is aimed at students with a background in basic linear algebra, analysis, statistics, and probability.

We encourage students who are interested in mathematical data science to take both this course and "401-4944-20L Mathematics of Data Science" by Prof. A. Bandeira. The two courses are designed to be complementary.

H. Bölcskei and A. Bandeira
261-5110-00LOptimization for Data Science Information W8 KP3V + 2U + 2AB. Gärtner, D. Steurer
KurzbeschreibungThis course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in data science.
LernzielUnderstanding the theoretical guarantees (and their limits) of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science.
InhaltThis course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in machine learning and data science.

In the first part of the course, we will first give a brief introduction to convex optimization, with some basic motivating examples from machine learning. Then we will analyse classical and more recent first and second order methods for convex optimization: gradient descent, projected gradient descent, subgradient descent, stochastic gradient descent, Nesterov's accelerated method, Newton's method, and Quasi-Newton methods. The emphasis will be on analysis techniques that occur repeatedly in convergence analyses for various classes of convex functions. We will also discuss some classical and recent theoretical results for nonconvex optimization.

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.
Voraussetzungen / BesonderesAs 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.
252-0220-00LIntroduction to Machine Learning Information Belegung eingeschränkt - Details anzeigen
Limited number of participants. Preference is given to students in programmes in which the course is being offered. All other students will be waitlisted. Please do not contact Prof. Krause for any questions in this regard. If necessary, please contact Link
W8 KP4V + 2U + 1AA. Krause
KurzbeschreibungThe course introduces the foundations of learning and making predictions based on data.
LernzielThe course will introduce the foundations of learning and making predictions from data. We will study basic concepts such as trading goodness of fit and model complexitiy. We will discuss important machine learning algorithms used in practice, and provide hands-on experience in a course project.
Inhalt- Linear regression (overfitting, cross-validation/bootstrap, model selection, regularization, [stochastic] gradient descent)
- Linear classification: Logistic regression (feature selection, sparsity, multi-class)
- Kernels and the kernel trick (Properties of kernels; applications to linear and logistic regression); k-nearest neighbor
- Neural networks (backpropagation, regularization, convolutional neural networks)
- Unsupervised learning (k-means, PCA, neural network autoencoders)
- The statistical perspective (regularization as prior; loss as likelihood; learning as MAP inference)
- Statistical decision theory (decision making based on statistical models and utility functions)
- Discriminative vs. generative modeling (benefits and challenges in modeling joint vy. conditional distributions)
- Bayes' classifiers (Naive Bayes, Gaussian Bayes; MLE)
- Bayesian approaches to unsupervised learning (Gaussian mixtures, EM)
LiteraturTextbook: Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press
Voraussetzungen / BesonderesDesigned to provide a basis for following courses:
- Advanced Machine Learning
- Deep Learning
- Probabilistic Artificial Intelligence
- Seminar "Advanced Topics in Machine Learning"
252-0526-00LStatistical Learning Theory Information W7 KP3V + 2U + 1AJ. M. Buhmann, C. Cotrini Jimenez
KurzbeschreibungThe course covers advanced methods of statistical learning:

- Variational methods and optimization.
- Deterministic annealing.
- Clustering for diverse types of data.
- Model validation by information theory.
LernzielThe course surveys recent methods of statistical learning. The fundamentals of machine learning, as presented in the courses "Introduction to Machine Learning" and "Advanced Machine Learning", are expanded from the perspective of statistical learning.
Inhalt- Variational methods and optimization. We consider optimization approaches for problems where the optimizer is a probability distribution. We will discuss concepts like maximum entropy, information bottleneck, and deterministic annealing.

- Clustering. This is the problem of sorting data into groups without using training samples. We discuss alternative notions of "similarity" between data points and adequate optimization procedures.

- Model selection and validation. This refers to the question of how complex the chosen model should be. In particular, we present an information theoretic approach for model validation.

- Statistical physics models. We discuss approaches for approximately optimizing large systems, which originate in statistical physics (free energy minimization applied to spin glasses and other models). We also study sampling methods based on these models.
SkriptA draft of a script will be provided. Lecture slides will be made available.
LiteraturHastie, 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
Voraussetzungen / BesonderesKnowledge of machine learning (introduction to machine learning and/or advanced machine learning)
Basic knowledge of statistics.
252-3900-00LBig Data for Engineers Information
This course is not intended for Computer Science and Data Science MSc students!
W6 KP2V + 2U + 1AG. Fourny
KurzbeschreibungThis course is part of the series of database lectures offered to all ETH departments, together with Information Systems for Engineers. It introduces the most recent advances in the database field: how do we scale storage and querying to Petabytes of data, with trillions of records? How do we deal with heterogeneous data sets? How do we deal with alternate data shapes like trees and graphs?
LernzielThis lesson is complementary with Information Systems for Engineers as they cover different time periods of database history and practices -- you can even take both lectures at the same time.

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.

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.
InhaltThis course gives an overview of database technologies and of the most important database design principles that lay the foundations of the Big Data universe.

It targets specifically students with a scientific or Engineering, but not Computer Science, background.

We take the monolithic, one-machine relational stack from the 1970s, smash it down and rebuild it on top of large clusters: starting with distributed storage, and all the way up to syntax, models, validation, processing, indexing, and querying. 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.

No data is harmed during this course, however, please be psychologically prepared that our data may not always be in normal form.

- physical storage: distributed file systems (HDFS), object storage(S3), key-value stores

- logical storage: document stores (MongoDB), column stores (HBase)

- data formats and syntaxes (XML, JSON, RDF, CSV, YAML, protocol buffers, Avro)

- data shapes and models (tables, trees)

- 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, JSONiq)

- 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)

- 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.
LiteraturPapers from scientific conferences and journals. References will be given as part of the course material during the semester.
Voraussetzungen / BesonderesThis course is not intended for Computer Science and Data Science students. Computer Science and Data Science students interested in Big Data MUST attend the Master's level Big Data lecture, offered in Fall.

Requirements: programming knowledge (Java, C++, Python, PHP, ...) as well as basic knowledge on databases (SQL). If you have already built your own website with a backend SQL database, this is perfect.

Attendance is especially recommended to those who attended Information Systems for Engineers last Fall, which introduced the "good old databases of the 1970s" (SQL, tables and cubes). However, this is not a strict requirement, and it is also possible to take the lectures in reverse order.
263-5300-00LGuarantees for Machine Learning Information Belegung eingeschränkt - Details anzeigen W5 KP2V + 2AF. Yang
KurzbeschreibungThis course teaches classical and recent methods in statistics and optimization commonly used to prove theoretical guarantees for machine learning algorithms. The knowledge is then applied in project work that focuses on understanding phenomena in modern machine learning.
LernzielThis course is aimed at advanced master and doctorate students who want to understand and/or conduct independent research on theory for modern machine learning. For this purpose, students will learn common mathematical techniques from statistical learning theory. In independent project work, they then apply their knowledge and go through the process of critically questioning recently published work, finding relevant research questions and learning how to effectively present research ideas to a professional audience.
InhaltThis course teaches some classical and recent methods in statistical learning theory aimed at proving theoretical guarantees for machine learning algorithms, including topics in

- concentration bounds, uniform convergence
- high-dimensional statistics (e.g. Lasso)
- prediction error bounds for non-parametric statistics (e.g. in kernel spaces)
- minimax lower bounds
- regularization via optimization

The project work focuses on active theoretical ML research that aims to understand modern phenomena in machine learning, including but not limited to

- how overparameterization could help generalization ( interpolating models, linearized 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 )
- prediction with calibrated confidence ( conformal prediction, calibration )
Voraussetzungen / BesonderesIt’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”. It's also helpful to have heard an optimization course or approximation theoretic course. 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.
636-0702-00LStatistical Models in Computational BiologyW6 KP2V + 1U + 2AN. Beerenwinkel
KurzbeschreibungThe course offers an introduction to graphical models and their application to complex biological systems. Graphical models combine a statistical methodology with efficient algorithms for inference in settings of high dimension and uncertainty. The unifying graphical model framework is developed and used to examine several classical and topical computational biology methods.
LernzielThe goal of this course is to establish the common language of graphical models for applications in computational biology and to see this methodology at work for several real-world data sets.
InhaltGraphical models are a marriage between probability theory and graph theory. They combine the notion of probabilities with efficient algorithms for inference among many random variables. Graphical models play an important role in computational biology, because they explicitly address two features that are inherent to biological systems: complexity and uncertainty. We will develop the basic theory and the common underlying formalism of graphical models and discuss several computational biology applications. Topics covered include conditional independence, Bayesian networks, Markov random fields, Gaussian graphical models, EM algorithm, junction tree algorithm, model selection, Dirichlet process mixture, causality, the pair hidden Markov model for sequence alignment, probabilistic phylogenetic models, phylo-HMMs, microarray experiments and gene regulatory networks, protein interaction networks, learning from perturbation experiments, time series data and dynamic Bayesian networks. Some of the biological applications will be explored in small data analysis problems as part of the exercises.
Skriptno
Literatur- Airoldi EM (2007) Getting started in probabilistic graphical models. PLoS Comput Biol 3(12): e252. doi:10.1371/journal.pcbi.0030252
- Bishop CM. Pattern Recognition and Machine Learning. Springer, 2007.
- Durbin R, Eddy S, Krogh A, Mitchinson G. Biological Sequence Analysis. Cambridge university Press, 2004
701-0104-00LStatistical Modelling of Spatial DataW3 KP2GA. J. Papritz
KurzbeschreibungIn 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.
LernzielThe 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.
InhaltAfter 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.
SkriptSlides, descriptions of the problems for the data analyses and solutions to them will be provided.
LiteraturP.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer.

Bivand, R. S., Pebesma, E. J. & Gómez-Rubio, V. 2013. Applied Spatial Data Analysis with R. Springer.
Voraussetzungen / BesonderesFamiliarity 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.
401-6222-00LRobust and Nonlinear Regression Information Belegung eingeschränkt - Details anzeigen W2 KP1V + 1UA. F. Ruckstuhl
KurzbeschreibungIn a first part, the basic ideas of robust fitting techniques are explained theoretically and practically using regression models and explorative multivariate analysis.

The second part addresses the challenges of fitting nonlinear regression functions and finding reliable confidence intervals.
LernzielParticipants are familiar with common robust fitting methods for the linear regression models as well as for exploratory multivariate analysis and are able to assess their suitability for the data at hand.

They know the challenges that arise in fitting of nonlinear regression functions, and know the difference between classical and profile based methods to determine confidence intervals.

They can apply the discussed methods in practise by using the statistics software R.
InhaltRobust fitting: influence function, breakdown point, regression M-estimation, regression MM-estimation, robust inference, covariance estimation with high breakdown point, application in principal component analysis and linear discriminant analysis.

Nonlinear regression: the nonlinear regression model, estimation methods, approximate tests and confidence intervals, estimation methods, profile t plot, profile traces, parameter transformation, prediction and calibration
SkriptLecture notes are available
Voraussetzungen / BesonderesIt is a block course on three Mondays in June
401-8618-00LStatistical Methods in Epidemiology (University of Zurich)
Der Kurs muss direkt an der UZH belegt werden.
UZH Modulkürzel: STA408

Beachten Sie die Einschreibungstermine an der UZH: Link
W5 KP3GUni-Dozierende
KurzbeschreibungAnalysis of case-control and cohort studies. The most relevant measures
of effect (odds and rate ratios) are introduced, and methods for
adjusting for confounders (Mantel-Haenszel, regression) are thoroughly
discussed. Advanced topics such as measurement error and propensity
score adjustments are also covered. We will outline statistical methods
for case-crossover and case series studies etc.
Lernziel
401-4626-00LAdvanced Statistical Modelling: Mixed ModelsW4 KP2VM. Mächler
KurzbeschreibungMixed Models = (*| generalized| non-) linear Mixed-effects Models, extend traditional regression models by adding "random effect" terms.

In applications, such models are called "hierarchical models", "repeated measures" or "split plot designs". Mixed models are widely used and appropriate in an aera of complex data measured from living creatures from biology to human sciences.
Lernziel- Becoming aware how mixed models are more realistic and more powerful in many cases than traditional ("fixed-effects only") regression models.

- Learning to fit such models to data correctly, critically interpreting results for such model fits, and hence learning to work the creative cycle of responsible statistical data analysis:
"fit -> interpret & diagnose -> modify the fit -> interpret & ...."

- Becoming aware of computational and methodological limitations of these models, even when using state-of-the art software.
InhaltThe lecture will build on various examples, use R and notably the `lme4` package, to illustrate concepts. The relevant R scripts are made available online.

Inference (significance of factors, confidence intervals) will focus on the more realistic *un*balanced situation where classical (ANOVA, sum of squares etc) methods are known to be deficient. Hence, Maximum Likelihood (ML) and its variant, "REML", will be used for estimation and inference.
SkriptWe will work with an unfinished book proposal from Prof Douglas Bates, Wisconsin, USA which itself is a mixture of theory and worked R code examples.

These lecture notes and all R scripts are made available from
Link
Literatur(see web page and lecture notes)
Voraussetzungen / Besonderes- We assume a good working knowledge about multiple linear regression ("the general linear model') and an intermediate (not beginner's) knowledge about model based statistics (estimation, confidence intervals,..).

Typically this means at least two classes of (math based) statistics, say
1. Intro to probability and statistics
2. (Applied) regression including Matrix-Vector notation Y = X b + E

- Basic (1 semester) "Matrix calculus" / linear algebra is also assumed.

- If familiarity with [R](Link) is not given, it should be acquired during the course (by the student on own initiative).
447-6236-00LStatistics for Survival Data Belegung eingeschränkt - Details anzeigen W2 KP1V + 1UA. Hauser
KurzbeschreibungThe primary purpose of a survival analysis is to model and analyze time-to-event data; that is, data that have as a principal endpoint the length of time for an event to occur. This block course introduces the field of survival analysis without getting too embroiled in the theoretical technicalities.
LernzielPresented here are some frequently used parametric models and methods, including accelerated failure time models; and the newer nonparametric procedures which include the Kaplan-Meier estimate of survival and the Cox proportional hazards regression model. The statistical tools treated are applicable to data from medical clinical trials, public health, epidemiology, engineering, economics, psychology, and demography as well.
InhaltThe primary purpose of a survival analysis is to model and analyze time-to-event data; that is, data that have as a principal endpoint the length of time for an event to occur. Such events are generally referred to as "failures." Some examples are time until an electrical component fails, time to first recurrence of a tumor (i.e., length of remission) after initial treatment, time to death, time to the learning of a skill, and promotion times for employees.

In these examples we can see that it is possible that a "failure" time will not be observed either by deliberate design or due to random censoring. This occurs, for example, if a patient is still alive at the end of a clinical trial period or has moved away. The necessity of obtaining methods of analysis that accommodate censoring is the primary reason for developing specialized models and procedures for failure time data. Survival analysis is the modern name given to the collection of statistical procedures which accommodate time-to-event censored data. Prior to these new procedures, incomplete data were treated as missing data and omitted from the analysis. This resulted in the loss of the partial information obtained and in introducing serious systematic error (bias) in estimated quantities. This, of course, lowers the efficacy of the study. The procedures discussed here avoid bias and are more powerful as they utilize the partial information available on a subject or item.

This block course introduces the field of survival analysis without getting too embroiled in the theoretical technicalities. Models for failure times describe either the survivor function or hazard rate and their dependence on explanatory variables. Presented here are some frequently used parametric models and methods, including accelerated failure time models; and the newer nonparametric procedures which include the Kaplan-Meier estimate of survival and the Cox proportional hazards regression model. The statistical tools treated are applicable to data from medical clinical trials, public health, epidemiology, engineering, economics, psychology, and demography as well.
401-8628-00LSurvival Analysis (University of Zurich)
Der Kurs muss direkt an der UZH belegt werden.
UZH Modulkürzel: STA425

Beachten Sie die Einschreibungstermine an der UZH: Link
W3 KP1.5GUni-Dozierende
KurzbeschreibungThe analysis of survival times, or in more general terms, the analysis
of time to event variables is concerned with models for censored
observations. Because we cannot always wait until the event of interest
actually happens, the methods discussed here are required for an
appropriate handling of incomplete observations where we only know that
the event of interest did not happen within ...
Lernziel
InhaltDuring the course, we will study the most important methods and models
for censored data, including
- general concepts of censoring,
- simple summary statistics,
- estimation of survival curves,
- frequentist inference for two and more groups, and
- regression models for censored observations