Suchergebnis: Katalogdaten im Frühjahrssemester 2020

Cyber Security Master Information
Ergänzung
Theoretical Computer Science
Kernfächer
NummerTitelTypECTSUmfangDozierende
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.
Wahlfächer
NummerTitelTypECTSUmfangDozierende
252-1424-00LModels of ComputationW6 KP2V + 2U + 1AM. Cook
KurzbeschreibungThis course surveys many different models of computation: Turing Machines, Cellular Automata, Finite State Machines, Graph Automata, Circuits, Tilings, Lambda Calculus, Fractran, Chemical Reaction Networks, Hopfield Networks, String Rewriting Systems, Tag Systems, Diophantine Equations, Register Machines, Primitive Recursive Functions, and more.
LernzielThe goal of this course is to become acquainted with a wide variety of models of computation, to understand how models help us to understand the modeled systems, and to be able to develop and analyze models appropriate for new systems.
InhaltThis course surveys many different models of computation: Turing Machines, Cellular Automata, Finite State Machines, Graph Automata, Circuits, Tilings, Lambda Calculus, Fractran, Chemical Reaction Networks, Hopfield Networks, String Rewriting Systems, Tag Systems, Diophantine Equations, Register Machines, Primitive Recursive Functions, and more.
272-0302-00LApproximations- und Online-Algorithmen Information W5 KP2V + 1U + 1AH.‑J. Böckenhauer, D. Komm
KurzbeschreibungDiese Lerneinheit behandelt approximative Verfahren für schwere Optimierungsprobleme und algorithmische Ansätze zur Lösung von Online-Problemen sowie die Grenzen dieser Ansätze.
LernzielAuf systematische Weise einen Überblick über die verschiedenen Entwurfsmethoden von approximativen Verfahren für schwere Optimierungsprobleme und Online-Probleme zu gewinnen. Methoden kennenlernen, die Grenzen dieser Ansätze aufweisen.
InhaltApproximationsalgorithmen sind einer der erfolgreichsten Ansätze zur Behandlung schwerer Optimierungsprobleme. Dabei untersucht man die sogenannte Approximationsgüte, also das Verhältnis der Kosten einer berechneten Näherungslösung und der Kosten einer (nicht effizient berechenbaren) optimalen Lösung.
Bei einem Online-Problem ist nicht die gesamte Eingabe von Anfang an bekannt, sondern sie erscheint stückweise und für jeden Teil der Eingabe muss sofort ein entsprechender Teil der endgültigen Ausgabe produziert werden. Die Güte eines Algorithmus für ein Online-Problem misst man mit der competitive ratio, also dem Verhältnis der Kosten der berechneten Lösung und der Kosten einer optimalen Lösung, wie man sie berechnen könnte, wenn die gesamte Eingabe bekannt wäre.

Inhalt dieser Lerneinheit sind
- die Klassifizierung von Optimierungsproblemen nach der erreichbaren Approximationsgüte,
- systematische Methoden zum Entwurf von Approximationsalgorithmen (z. B. Greedy-Strategien, dynamische Programmierung, LP-Relaxierung),
- Methoden zum Nachweis der Nichtapproximierbarkeit,
- klassische Online-Probleme wie Paging oder Scheduling-Probleme und Algorithmen zu ihrer Lösung,
- randomisierte Online-Algorithmen,
- Entwurfs- und Analyseverfahren für Online-Algorithmen,
- Grenzen des "competitive ratio"- Modells und Advice-Komplexität als eine Möglichkeit, die Komplexität von Online-Problemen genauer zu messen.
LiteraturDie Vorlesung orientiert sich teilweise an folgenden Büchern:

J. Hromkovic: Algorithmics for Hard Problems, Springer, 2004

D. Komm: An Introduction to Online Computation: Determinism, Randomization, Advice, Springer, 2016

Zusätzliche Literatur:

A. Borodin, R. El-Yaniv: Online Computation and Competitive Analysis, Cambridge University Press, 1998
263-4400-00LAdvanced Graph Algorithms and Optimization Information Belegung eingeschränkt - Details anzeigen
Number of participants limited to 30.
W5 KP3G + 1AR. Kyng
KurzbeschreibungThis course will cover a number of advanced topics in optimization and graph algorithms.
LernzielThe 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.
InhaltStudents 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 / BesonderesThis 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.
401-3052-05LGraph Theory Information W5 KP2V + 1UB. Sudakov
KurzbeschreibungBasic notions, trees, spanning trees, Caley's formula, vertex and edge connectivity, 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
LernzielThe 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.
SkriptLecture will be only at the blackboard.
LiteraturWest, D.: "Introduction to Graph Theory"
Diestel, R.: "Graph Theory"

Further literature links will be provided in the lecture.
Voraussetzungen / BesonderesStudents are expected to have a mathematical background and should be able to write rigorous proofs.


NOTICE: This course unit was previously offered as 252-1408-00L Graphs and Algorithms.
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)
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