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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Mathematics for data science

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Code Completion Credits Range Language
MI-MZI Z,ZK 4 2+1 Czech
Lecturer:
Daniel Vašata, Štěpán Starosta (guarantor), Karel Klouda
Tutor:
Daniel Vašata, Štěpán Starosta (guarantor), Karel Klouda
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:

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:
Time-table for winter semester 2018/2019:
Time-table is not available yet
Time-table for summer semester 2018/2019:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri
Thu
Fri
roomTH:A-1442
Klouda K.
Vašata D.

09:15–10:45
(lecture parallel1)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Klouda K.
Vašata D.

11:00–12:30
ODD WEEK

(lecture parallel1
parallel nr.101)

Thákurova 7 (FSv-budova A)
The course is a part of the following study plans:
Data valid to 2019-03-21
For updated information see http://bilakniha.cvut.cz/en/predmet4732806.html