Probabilistic Machine Learning (RO5101 T)

The lecture Probabilistic Machine Learning belongs to the Module Robot Learning (RO4100).

The lecture Probabilistic Machine Learning belongs to the Module Robot Learning (RO4100).

In the winter semester, Prof. Dr. Elmar Rueckert is teaching the course Probabilistic Machine Learning (RO5101 T).

In the summer semester, Prof. Dr. Elmar Rueckert is teaching the course Reinforcement Learning (RO5102 T).

Important: Due to the study regulations, students have to attend both lectures to receive a final grade. Thus, there will be only a single written exam for both lectures. You can register for the written exam at the end of a semester. Note that students are only allowed to attend the exam if they achieve at least 50 percent of the points for there assignments in each of the two accompanying exercises.

The book of this lecture can be found here:

The solutions for the exercises in the book can be found here:

A Latex Draft for the Assignments can be found here:

Note that this book and the solutions are work in progress and the pdfs will be constantly updated.

The course topics are

  1. Introduction to Probability Theory (Statistics refresher, Bayes Theorem, Common Probability distributions, Gaussian Calculus).
  2. Linear Probabilistic Regression (Linear models, Maximum Likelihood, Bayes & Logistic Regression).
  3. Nonlinear Probabilistic Regression (Radial basis function networks, Gaussian Processes, Recent research results in Robotic Movement Primitives, Hierarchical Bayesian & Mixture Models).
  4. Probabilistic Inference for Filtering, Smoothing and Planning (Classic, Extended & Unscented Kalman Filters, Particle Filters, Gibbs Sampling, Recent research results in Neural Planning).
  5. Probabilistic Optimization (Stochastic black-box Optimizer Covariance Matrix Analysis Evolutionary Strategies & Natural Evolutionary Strategies, Bayesian Optimization).

The learning objectives / qualifications are

  • Students get a comprehensive understanding of basic probability theory concepts and methods.
  • Students learn to analyze the challenges in a task and to identify promising machine learning approaches.
  • Students will understand the difference between deterministic and probabilistic algorithms and can define underlying assumptions and requirements.
  • Students understand and can apply advanced regression, inference and optimization techniques to real world problems.
  • Students know how to analyze the models’ results, improve the model parameters and can interpret the model predictions and their relevance.
  • Students understand how the basic concepts are used in current state-of-the-art research in robot movement primitive learning and in neural planning.

Follow this link to register for the course:

Location & Times


Strong statistical and mathematical knowledge is required beforehand. It is highly recommended to attend the course Humanoid Robotics (RO5300) prior to attending this course. The students will also experiment with state-of-the-art machine learning methods and robotic simulation tools which require strong programming skills.


The course is accompanied by regular tutorials, programming  exercises  and written assignments. The written assignments as well as the programming exercises will be graded. After the summer semester a single written exam for both lectures, probabilistic machine learning and reinforcement learning, has to be passed. Details will be presented in the first course unit on October the 17th, 2019.

Course dates & materials (tentative schedule)

Dates TopicsLinks
17.10.2019VOAn Introduction to the Probabilistic Machine Learning (PML) lectureSlides
24.10.2019VORandom Variables, Fundamental Rules
28.10.2019UERandom Variables, Fundamental Rules, Bayesian and Frequentist View
07.11.2019VO Fundamental Distributions, Information Theory
11.11.2019UEFundamental Distributions, Information Theory
14.11.2019VOLinear Regression, Bayesian Regression
18.11.2019UEROS Introduction,
Kalman Filter Tutorial
Slides Kalman Filter, Slides ROS
21.11.2019VOFundamental concepts: Overfitting, i.i.d., generative vs discriminative. Non-linear Bayesian Regression Slides, Python Code, Dataset
28.11.2019VOMarkov Models, Gaussian Processes, GMRFs
02.12.2019UELinear Probabilistic Regression
05.12.2019VOProbabilistic Inference
09.12.2019UESequential Online LearningMatlab Demo of Sequential Learning
12.12.2019VOProbabilistic Time Series ModelsMatlab Probabilistic Timer Series Model Demo
16.12.2019UEDeadline: Assignment Submissions and Discussions
19.12.2019VOBonus point exam where 10 pts can be received.
09.01.2020UEReview Bonus Exam
13.01.2020VOProbabilistic Trajectory ModelsSlides to Extensions of Probabilistic Time Series Models
16.01.2020UEGPs with builtin Markov Random Fields
20.01.2020UEProbabilistic Trajectory ModelsExercise Description Matlab Dataset, template and plotting function
23.01.2020VOMotion Planning
27.01.2020UEExam Questions
30.01.2020VOMotion Inference & Planning
03.02.2020UEAssignment Submissions and Discussions
06.02.2020VOQ & A for the final exam.
17.02.2020ExamDate of the written exam.
11.03.2020Exam, second optionDate of the written exam.

Prof. Dr. Elmar Rueckert
Teaching Assistant:
Nils Rottmann, M.Sc.
English only


  • Daphne Koller, Nir Friedman. Probabilistic Graphical Models: Principles and Techniques. ISBN 978-0-262-01319-2
  • Christopher M. Bishop. Pattern Recognition and Machine Learning. Springer (2006). ISBN 978-0-387-31073-2.
  • David Barber. Bayesian Reasoning and Machine Learning, Cambridge University Press (2012). ISBN 978-0-521-51814-7.
  • Kevin P. Murphy. Machine Learning: A Probabilistic Perspective. ISBN 978-0-262-01802-9

Materials for the exercise

The course is accompanied by three graded assignments on Probabilistic Regression, Probabilistic Inference and on Probabilistic Optimization. The assignments will include algorithmic implementations in Matlab, Python or C++ and will be presented during the exercise sessions. The Robot Operating System (ROS) will also be part in some assignments as well as the simulation environment Gazebo. To experiment with state-of-the-art robot control and learning methods Mathworks’ MATLAB will be used. If you do not have it installed yet, please follow the instructions of our IT-Service Center.

Materials for the Exam

Please have a look into the rules of Texas Holdem Poker. We will ask Question with regard to this game in the final exam. You can find an overview of the rules her: