Course details

Bayesian Models for Machine Learning (in English)

BAYa Acad. year 2022/2023 Winter semester 5 credits

Current academic year

Probability theory and probability distributions, Bayesian Inference, Inference in Bayesian models with conjugate priors, Inference in Bayesian Networks, Expectation-Maximization algorithm, Approximate inference in Bayesian models using Gibbs sampling, Variational Bayes inference, Stochastic VB, Infinite mixture models, Dirichlet Process, Chinese Restaurant Process, Pitman-Yor Process for Language modeling, Expectation propagation, Gaussian Process, Auto-Encoding Variational Bayes, Practical applications of Bayesian inference


Course coordinator

Language of instruction




Time span

  • 26 hrs lectures
  • 13 hrs exercises
  • 13 hrs projects

Assessment points

  • 51 pts final exam (written part)
  • 24 pts mid-term test (written part)
  • 25 pts projects




Learning objectives

To demonstrate the limitations of Deep Neural Nets (DNN) that have become a very popular machine learning tool successful in many areas, but that excel only when sufficient amount of well annotated training data is available. To present Bayesian models (BMs) allowing to make robust decisions even in cases of scarce training data as they take into account the uncertainty in the model parameter estimates. To introduce the concept of latent variables making BMs modular (i.e. more complex models can be built out of simpler ones) and well suitable for cases with missing data (e.g. unsupervised learning when annotations are missing). To introduce basic skills and intuitions about the BMs and to develop more advanced topics such as: approximate inference methods necessary for more complex models, infinite mixture models based on non-parametric BMs, or Auto-Encoding Variational Bayes. The course is taught in English.

Why is the course taught

Nothing in life is given for sure. The uncertainty is accompanying us also in machine learning, classification and recognition - in the basic courses, youll learn how to train parameters of Gaussian models or neural networks. But are they correct? Can we be sure about the result? How about if the model is deployed on data different from the training ones? The BAY course will teach you not to trust anything and express everything as probability distributions rather than hard numbers. You will enjoy lots of maths, but if you are serious about machine learning, you cant consider it just as "connecting black boxes". You need a solid mathematical background.

Study literature

Syllabus of lectures

  1. Probability theory and probability distributions 
  2. Bayesian Inference (priors, uncertainty of the parameter estimates, posterior predictive probability) 
  3. Inference in Bayesian models with conjugate priors 
  4. Inference in Bayesian Networks (loopy belief propagation) 
  5. Expectation-Maximization algorithm (with application to Gaussian Mixture Model) 
  6. Approximate inference in Bayesian models using Gibbs sampling 
  7. Variational Bayes inference, Stochastic VB 
  8. Infinite mixture models, Dirichlet Process, Chinese Restaurant Process 
  9. Pitman-Yor Process for Language modeling 
  10. Expectation propagation 
  11. Gaussian Process 
  12. Auto-Encoding Variational Bayes 
  13. Practical applications of Bayesian inference

Syllabus of numerical exercises

Lectures will be immediately followed by demonstration exercises where examples in Python will be presented. Code and data of all demonstrations will be made available to the students and will constitute the basis for the project.

Syllabus - others, projects and individual work of students

The project will follow on the demonstration exercises and will make the student work on provided (simulated or real) data. The students will work in teams in "evaluation" mode and present their results at the final lecture/exercise.

Progress assessment

  • Mid-term exam (24 points)  

  • Submission and presentation of project (25 points) 

  • Final exam (51points) 

To get points from the exam, you need to get min. 20 points, otherwise the exam is rated 0 points.

Course inclusion in study plans

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