Mathematics for data science
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| MI-MZI | Z,ZK | 4 | 2P+1C | Czech |
- Course guarantor:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Applied Mathematics
- Synopsis:
-
In this course, students are introduced to those fields of mathematics that are necessary for understanding standard methods and algorithms used in data science. The studied topics include mainly: linear algebra (matrix factorisations, eigenvalues, diagonalization), continuous optimisation (optimisation with constraints, duality principle, gradient methods) and selected notions from probability theory and statistics.
- Requirements:
-
Knowledge of basic notions of linear algebra and matrix theory, basics of probability theory, course MI-MPI: Mathematics for informatics.
- Syllabus of lectures:
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1) Mathematical formulation of regression and classification problem.
2) Geometrical view of linear regression model and least squares method (LS).
3) Computing the LS estimate (QR decomposition of a matrix).
4) Hypothesis tests for linear model, model validation.
5) Variable subset selection: ridge regression, best-subset selection, etc.
7) Singular value decomposition and its connection with ridge regression.
8) [2] Principal component analysis and dimensionality reduction.
10) Linear regression and classification.
11) Logistic regression.
12) Local regression and smoothing methods (splines, kernels).
13) [2] Support vector machines.
- Syllabus of tutorials:
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1) Least squares method.
2) Matrix factorisation and matrix eigenvalues.
3) Usage of linear regression and related methods.
4) Principal component analysis.
5) Logistic regression.
6) Support vector machines.
- Study Objective:
- Study materials:
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1. Christopher Bishop, Pattern Recognition and Machine Learning, Springer-Verlag New York (2006), ISBN 978-0-387-31073-2
2. Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer (2011), ISBN 978-0387848570.
- Note:
- Further information:
- https://courses.fit.cvut.cz/MI-MZI/
- No time-table has been prepared for this course
- The course is a part of the following study plans:
-
- Master branch Knowledge Engineering, in Czech, 2016-2017 (elective course)
- Master branch Computer Security, in Czech, 2016-2019 (elective course)
- Master branch Computer Systems and Networks, in Czech, 2016-2019 (elective course)
- Master branch Design and Programming of Embedded Systems, in Czech, 2016-2019 (elective course)
- Master branch Web and Software Engineering, spec. Info. Systems and Management, in Czech, 2016-2019 (elective course)
- Master branch Web and Software Engineering, spec. Software Engineering, in Czech, 2016-2019 (elective course)
- Master branch Web and Software Engineering, spec. Web Engineering, in Czech, 2016-2019 (elective course)
- Master program Informatics, unspecified branch, in Czech, version 2016-2019 (elective course)
- Master branch System Programming, spec. System Programming, in Czech, 2016-2019 (elective course)
- Master branch System Programming, spec. Computer Science, in Czech, 2016-2017 (elective course)
- Master specialization Computer Science, in Czech, 2018-2019 (elective course)
- Master branch Knowledge Engineering, in Czech, 2018-2019 (elective course)