Bayes Networks

General Information

This page contains information about the lecture "Bayes Networks" (in German "Bayes-Netze") that is held in winter term 2018/2019 by Prof. Dr. Rudolf Kruse. This page is updated during the course.


No Exercise Class on 22.01 and 23.01. We will have a combined exercise class during the lecture time slot on the 24.01.



  • Representation of uncertain information
  • Bayesian networks
  • Markov networks
  • Evidence propagation in probabilistic networks
  • Learning of probabilistic networks
  • Revision of probabilistic networks
  • Decision Graphs
  • Handling imprecise data and imprecise probabilities
  • Applications


Schedule and Rooms

Lecture Thursday 11.15-12.45 G29-307 11.10.2017 english
Exercise    Tuesday 09.15-10.45 G29-K059 16.10.2017 english
Exercise Wednesday 13.15-14.45 G29-E037 17.10.2017 english

Every student who wants to participate in the exercise must register her-/himself via the FIN Registration Service for the exercise. If you have any trouble with verifying the SSL certificate Jens Elkner could help you. While doing the registration, we kindly ask you to give an e-mail address of which incoming e-mail you check regularly.



If you have questions regarding the lecture or exercise, please contact (via e-mail if possible) one of the persons named below.


Conditions for Certificates (Scheine) and Exams

Certificate (Übungsschein): There are assignment sheets published every week. Assignments the solutions of which you want to present in the next exercise lecture have to be ticked beforehand on a votation sheet that is handed our prior to every exercise lecture. If ticked, you may be asked to present your solution in front of class. The solutions need not necessarily be completely correct, however, it should become obvious that you treated the assignment thoroughly. You are granted the certificate (Schein), if (and only if) you

  • ticked at least two thirds of the assignments,
  • presented at least two times a solution during the exercise, and
  • pass the exam

Exam: If you intend to finish the course with an exam, your are required to meet the certificate conditions. There will be a written exam after the curse. You can use your own not graphical and not programmable calculator.



You should have background knowledge on fundamentals of computer science such as algorithms, data structures etc. Also, insights into probability theory are highly recommended.



Note that the script may be subject to change (which will be stated in the news section above) during the course, i.e. page numbers may change.

Lecture 00 - Introduction

Lecture 01 - Rule-Based Systems

Lecture 02 - Probability Foundations

Lecture 03 - Decomposition

Lecture 04 - Separation Concepts (updated definition of the minimal ancestral subgraph)

Lecture 05 - Probabilistic Graphical Models

Lecture 06 - Inference in Belief Trees (corrected calculation of the pi component on slide 220 and 221)

Lecture 07 - Clique Tree Representations

Lecture 08 - Propagation in Clique Trees

Lecture 09 - Manual Building of Bayes Networks

Lecture 10 - Building Bayes Networks: Parameter Learning

Lecture 11 - Learning Decision Trees

Lecture 12 - Building Bayes Networks: Structure Learning

Lecture 13 - Revision

Lecture 14 - Decision Graphs

Lecture 15 - Hidden Markov Models

Assignment Sheets

The assignment sheets will be published weekly at this location.

Exercise Sheet 01 - Submission due to 16th/17th October

Exercise Sheet 02 - Submission due to 23rd/24th October

Exercise Sheet 03 - Submission due to 6th/7th November

Exercise Sheet 04 - Submission due to 13th/14th November

Exercise Sheet 05 - Submission due to 20th/21th November

Exercise Sheet 06 - Submission due to 27th/28th November

Exercise Sheet 07 - Submission due to 4th/5th December (see "Illustration of Simple Tree Propagation" in the Additional Material section for help)

Exercise Sheet 08 - Submission due to 11th/12th December (see "Joint Tree Propagation" in the Additional Material section for help)

no Exercise in the week of 1st and 2nd January

Exercise Sheet 09 - Submission due to 08th/09th January

Exercise Sheet 10 - Submission due to 15th/16th January

No Exercise Class on 22.01 and 23.01. We will have a combined exercise class during the lecture time slot on the 24.01.


Additional Material

Feel free to check out the following supplementary material that augment the lecture and exercise.



Here you find links to programs with for learning and using Bayesian networks.



  • Computational Intelligence - A Methodological Introduction
    Kruse, R., Borgelt, C., Braune, C., Mostaghim, S., Steinbrecher, M.
    Springer-Verlag London 2013, 2016
  • Graphical Models - Representations for Learning, Reasoning and Data Mining, 2nd Edition.
    C. Borgelt, M. Steinbrecher und R. Kruse.
    J. Wiley & Sons, Chichester, United Kingdom 2009
  • Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis
    Uffe B. Kjærulff, Anders L. Madsen
    Springer Science+Business Media New York 2013



Last Modification: 21.01.2019 - Contact Person:

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