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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

NI-PON Selected Topics in Optimization and Numerical mathematics Extent of teaching: 2P+1C
Instructor: Klouda K., Starosta Š., Vašata D. Completion: Z,ZK
Department: 18105 Credits: 5 Semester: L

Annotation:
The course focuses on optimization problems that appear in the field of machine learning and artificial intelligence. Students broaden their knowledge of continuous optimization obtained in the course Mathematics for informatics. The methods are explained and described along with the details on how they are implemented on computers. Hence, the relevant concepts of numerical matematics, mainly numerical linear algebra, are explained too.

Lecture syllabus:
1. Continuous optimization: problem statement and machine learning examples.
2.-3.  (2) Iterative methods for finding local extremal values (gradient descent, Newton's method, and their variants).
4. Lagrange method, Karush?Kuhn?Tucker conditions.
5. Duality and interior point method.
6.-7.  (2) QR decomposition, algorithms computing QR decomposition, QR algorithm.
8.-9.  (2) Linear regression and least squares method: statistical and numerical properties.
10.-11.  (2) Support Vector Machines regression.
12.-13.  (2) Matrix factorizations and their usage in machine learning (SVD, PCA, non-negative factorization).

Seminar syllabus:
1. Iterative methods for local extrema
2. Constrained optimization
3. Duality
4. Matrix factorizations
5. SVD, PCA
6. SVM

Literature:
1. Christopher Bishop, Pattern Recognition and Machine Learning, Springer-Verlag New York, 2006
2. Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, 2011.
3. Stephen Boyd, Lieven Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
4. Lloyd N. Trefethen, David Bau, Numerical Linear Algebra, SIAM: Society for Industrial and Applied Mathematics, 1997

Requirements:
NIE-MPI

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The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-PSS.2020 Computer Systems and Networks V 2
NI-SP.2020 System Programming V 2
NI-SP.2023 System Programming V 2
NI-SPOL.2020 Unspecified Branch/Specialisation of Study VO 2
NI-MI.2020 Managerial Informatics V 2
NI-TI.2023 Computer Science V 2
NI-TI.2020 Computer Science V 2
NI-NPVS.2020 Design and Programming of Embedded Systems V 2
NIE-DBE.2023 Digital Business Engineering VO 2
NI-PB.2020 Computer Security V 2
NI-SI.2020 Software Engineering (in Czech) V 2
NI-WI.2020 Web Engineering V 2
NI-ZI.2020 Knowledge Engineering PS 2
NI-SPOL.2020 Unspecified Branch/Specialisation of Study V 2


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška