Mathematics for data science

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

In this course, the students are introduced to the domains of mathematics necessary for understanding the 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 MIE-MPI: Mathematics for informatics.

Syllabus of lectures:

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:

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:

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 specialization Software Engineering, in English, 2021 (elective course)
• Master specialization Computer Security, in English, 2021 (elective course)
• Master specialization Computer Systems and Networks, in English, 2021 (elective course)
• Master specialization Design and Programming of Embedded Systems, in English, 2021 (elective course)
• Master specialization Computer Science, in English, 2021 (elective course)
• Study plan for Ukrainian refugees (elective course)
• Master Specialization Digital Business Engineering, 2023 (elective course)
• Master Programme Informatics, unspecified Specialization, in English, 2021 (elective course)
• Master specialization Computer Science, in English, 2024 (elective course)