Modulinformationssystem Informatik

 

Optimization and Data Science URL PDF XML

Modulcode: infODS-01a
Englische Bezeichnung: Optimization and Data Science
Modulverantwortliche(r): Prof. Dr. Thomas Slawig
Turnus: unregelmäßig (SS19 SS20 SS21)
Präsenzzeiten: 4V 2Ü
ECTS: 8
Workload: 60 h lectures, 30 h group excercise, 150 h self-study and home exercise
Dauer: ein Semester
Modulkategorien: BSc-Inf-WP (BSc Inf (21)) WI (BSc Inf (15)) MSc-Inf-WP (MSc Inf (21)) 2F-MEd-Inf-WP (MEd-Hdl Inf (21)) 2F-MA-Inf-WP (2F-MA Inf (21)) MSc-WInf-WP-WInf (MSc WInf (21)) WI (MSc Inf (15)) WI (MSc WInf (15)) WiWi (MSc WInf)
Lehrsprache: Englisch
Voraussetzungen: Info Inf-Math-A Inf-Math-B Inf-Math-C Inf-ProgOO

Kurzfassung:

Theory and algorithms for optimization problems used in data science and in general.

Lernziele:

The students are able to

  • explain and apply important methods of data analysis and data reduction
  • formulate and understand necessary and sufficient optimality conditions for unconstrained and constrained optimization problems
  • apply these criteria to exemplary problems
  • describe, implement and apply main algorithms of gradient-based and evolutionary optimization methods
  • assess these methods wrt. convergence, effort and applicability for different problems
  • assess and apply software libraries
  • understand the importance of optimization methods in data science

Lehrinhalte:

  • Methods of data analysis: Fourier transform, principal component analysis, regression, stochastic analysis
  • Optimality conditions for unconstrained optimization problems
  • Gradient-based optimization algorithms
  • Methods to compute or approximate derivatives
  • Optimization aspects of neural networks
  • Evolution strategies for optimization
  • Optimality conditions for constrained problems

Weitere Voraussetzungen:

  • Programming skills in a higher language
  • Good mathematical background (multi-dimensional calculus, linear algebra, basic stochastics)
  • Mathematic in Computer Science C is recommended

Prüfungsleistung:

Oral exam

Lehr- und Lernmethoden:

Flipped classroom method:

  • Self-study of content provided in video podcasts and slides
  • "lecture" hours are used for discussion of questions, examples and exercises
  • Additional exercise in groups
  • Homework exercises
  • Self-study

Verwendbarkeit:

According to the subject examination regulations for the Master's degree programme in Business Information Technology starting with WS 2021/22, the module is credited in the elective area of Business Information Technology for this Master's degree program. For students according to the subject examination regulations valid before, the credit will be awarded in the area of computer science.

Literatur:

  • S. l. Brunton, J.N. Kutz: Data-driven science and engineering, Cambridge University Press 2019.
  • C.T. Kelley: Iterative Methods for Optimization, SIAM 1999, can be found online at SIAM webpage.
  • L. Battou, F. E. Curtis, J. Nocedal: Optimization Methods for Large-Scale Machine Learning, in SIAM Review 60 (2), 2018 (online available from CAU network)
  • D.G. Luenberger, Y. Ye. Linear and nonlinear programming. 4th ed. Springer 2016.
  • J. Nocedal, S.J. Wright. Numerical optimization. 2nd ed. Springer 2006.
  • P.E. Gill, W. Murray, M.H. Wright: Practical Optimization, Academic Press 2nd ed. 1988.
  • W. Alt. Nichtlineare Optimierung. Eine Einführung in Theorie, Verfahren und Anwendungen. Vieweg, August 2002.
  • A. R. Conn, N. I. M. Gould, and P. L. Toint. Trust-region methods. MPS-SIAM series on optimization. Society for Industrial and Applied Mathematics, Philadelphia, 2000.
  • J.E. Dennis and R.B. Schnabel. Numerical methods for unconstrained optimization and nonlinear equations. SIAM, 1996.
  • P. Spellucci. Numerische Verfahren der nichtlinearen Optimierung. Birkhäuser, Basel, 1993.
  • J. Werner. Numerische Mathematik 1. Vieweg Studium, Aufbaukurs Mathematik. Vieweg, 1992
  • J. Werner. Numerische Mathematik 2. Vieweg Studium, Aufbaukurs Mathematik. Vieweg, 1992.

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