Bayesian Methods for Machine Learning

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

The subject is focused on practical use of basic Bayesian modeling methods in the dynamically evolving machine learning theory. In particular, it studies the construction of appropriate models providing description of real phenomena, as well as their subsequent use, e.g., for forecasting of future evolution or learning about the hidden variables (true object position from noisy observations etc.). The emphasis is put on understanding of explained principles and methods and their practical adoption. For this purpose, a number of real world examples and applications will be presented to students, for instance, 2D/3D object tracking, radiation source term estimation, or separation in medical imaging. The students will try to solve some of them.

Requirements:

Basic knowledge of probability theory and linear algebra.

Syllabus of lectures:

1. Basics and details of the Bayesian theory - uncertainty, knowledge evolution, types of estimates, methods.

2. Linear models in machine learning, online modeling, prediction, examples.

3. Generalized linear models GLM, approximation and sequential (online) estimation.

4. Linear model, structure estimation, prior-based regularization.

5. Bilinear models and Bayesian approach to PCA, estimation of the number of components.

6. Application of generalized linear models in real machine learning problems.

7. Basic state-space models, Kalman filter.

8. Introduction into Monte Carlo methods, rejection sampling.

9. Sequential Monte Carlo estimation of state-space models, bootstrap particle filter, resampling.

10. Hierarchical learning and its applications.

11. Graphical models, naive Bayes.

12. Introduction to deep learning and probabilistic graphical models.

Syllabus of tutorials:

1. Introduction, construction of a linear model and its estimation, knowledge evolution, forecasting.

2. Bayesian sequential linear regression, regularization, demonstrations on real data.

3. Sequential logistic regression with real data.

4. Bayesian matrix decomposition problem and its application, e.g., in biomedicine.

5. Construction of a state-space model for a real world problem and its estimation.

6. Particle filtration in practical problems of machine learning.

Study Objective:

The aim of the subject is to introduce the students to the wide application field of the Bayesian theory in machine learning.

Study materials:

1. Andrew Gelman et al., Bayesian Data Analysis, Chapman and Hall (2013), ISBN 1439840954.

2. David Barber, Bayesian Reasoning and Machine Learning, Cambridge University Press (2012), ISBN 978-0-521-51814-7.

Note:

Further information:

https://courses.fit.cvut.cz/NI-BML/

No time-table has been prepared for this course

The course is a part of the following study plans:

• Master specialization Computer Science, in Czech, 2018-2019 (elective course)
• Master specialization Computer Security, in Czech, 2020 (elective course)
• Master specialization Design and Programming of Embedded Systems, in Czech, 2020 (elective course)
• Master specialization Computer Systems and Networks, in Czech, 202 (elective course)
• Master specialization Management Informatics, in Czech, 2020 (elective course)
• Master specialization Software Engineering, in Czech, 2020 (elective course)
• Master specialization System Programming, in Czech, version from 2020 (elective course)
• Master specialization Web Engineering, in Czech, 2020 (elective course)
• Master specialization Knowledge Engineering, in Czech, 2020 (PS)
• Master specialization Computer Science, in Czech, 2020 (elective course)
• Mgr. programme, for the phase of study without specialisation, ver. for 2020 and higher (VO, elective course)
• Master Specialization Digital Business Engineering, 2023 (VO)
• Master specialization System Programming, in Czech, version from 2023 (elective course)
• Master specialization Computer Science, in Czech, 2023 (elective course)