Hierarchical Bayesian Models

Course guarantor:

Václav Šmídl

Lecturer:

Tutor:

Václav Šmídl

Supervisor:

Department of Mathematics

Synopsis:

Keywords:

Bayesian theory, linear regression, signal separation, mixture models, Bayesian filtering

Requirements:

Syllabus of lectures:

1. Fundamentals of Bayesian theory

2. Methods of approximate evaluation of Bayesian calculus (Variational Bayes, Importance Sampling, Gibbs Sampling)

3. Linear regression and structure selection algorithms (spike and slab, horseshoe prior, lasso, fused lasso, automatic relevance determination)

4. Signal separation and its variants as different prior models

5. Mixture models for clustering (using Gaussian and Beta components)

6. Estimation of relevant number of components in a mixture

7. Density representation in high dimensions (mixtures of factor analyzers, deep neural networks)

8. Bayesian filtering (Kalman and particle filter)

Syllabus of tutorials:

Study Objective:

Acquired knowledge:

Computational methods suitable for evaluation of hierarchical Bayesian models. Selected hierarchical models for common practical tasks. Relation of these models to classical approaches.

Acquired skills:

Ability to modify standard models to nonstandard problem formulations, incorporation of additional assumption into the model, development of computational method for the modified model

Study materials:

Compulsory literature:

[1] Bishop, C., Pattern Recognition and Machine Learning" Springer, New York, 2007.

Optional literature:

[2] Šmídl, Václav, and Anthony Quinn. The Variational Bayes Method in Signal Processing, Springer 2005.

Working environment:

Matlab

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikované matematicko-stochastické metody (elective course)