Mathematics for data science
- Department of Applied Mathematics
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.
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)  Principal component analysis and dimensionality reduction.
10) Linear regression and classification.
11) Logistic regression.
12) Local regression and smoothing methods (splines, kernels).
13)  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.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
- Computer Security, Presented in English, Version 2016 to 2019 (elective course)
- Computer Systems and Networks, Presented in English, Version 2016 to 2019 (elective course)
- Design and Programming of Embedded Systems, in English, Version 2016 to 2019 (elective course)
- Specialization Software Engineering, in English, Version 2016 to 2019 (elective course)