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2026/2027  KAN-CMECV2601U  Probabilistic Machine Learning

English Title
Probabilistic Machine Learning

Course information
Language English
Course ECTS 7.5 ECTS
Type Elective
Level Full Degree Master
Duration One Semester
Start time of the course Spring
Timetable Course schedule will be posted at calendar.cbs.dk
Study board
Study Board for Finance, Economics & Mathematics
Programme MSc in Business Administration and Mathematical Business Economics
Course coordinator
  • Anders Rønn-Nielsen - Department of Finance (FI)
Main academic disciplines
  • Mathematics
  • Statistics and quantitative methods
Teaching methods
  • Blended learning
Last updated on 26-01-2026

Relevant links
Learning objectives
At the end of the course, students are expected to be able to
  • Explain the concept of Bayesian statistics and how it differs from frequentist statistics
  • Understand, choose between and apply Graphical models and Bayesian networks to model dependence structures in data
  • Under and apply models with latent variables to describe complex random phenomena
  • Use MC-methods and MCMC-algorithms to do estimation and inferences in complex statistical models within a Bayesian setting
  • Use the EM-algorithm to make inference in models with latent variables
  • Communicate the results of an analysis performed with probabilistic machine learning methods
Course prerequisites
BA-BMECO1801U Sandsynlighedsteori (Probability Theory) and BA-BMECO1802U Matematisk statistik (Mathematical Statistics) or similar courses.
Examination
Probabilistic Machine Learning:
Exam ECTS 7,5
Examination form Oral exam
Individual or group exam Individual exam
Duration 30 min. per student, including examiners' discussion of grade, and informing plus explaining the grade
Preparation time No preparation
Grading scale 7-point grading scale
Examiner(s) Internal examiner and second internal examiner
Exam period Summer
Make-up exam/re-exam
Same examination form as the ordinary exam
Description of the exam procedure

First at the oral exam, a topic is drawn (randomly) from a list of known topics and the student gives a presentation on the topic. The student is expected to include relevant applications to real data in the presentation. After the presentation there will be an examination in the general curriculum.
Course content, structure and pedagogical approach

The course provides an introduction to probabilistic machine learning. During the course, the focus is going to be on the understanding of the methods and their theoretical foundations, as well as on concrete data applications of the various methods.

 

Specifically, the course covers the following topics:

  • Bayesian statistics
  • Graphical models
  • Bayesian networks and decision trees
  • Inference for models with latent variables
  • MC-methods
  • MCMC-algorithms
  • EM-algorithm
Research-based teaching
CBS’ programmes and teaching are research-based. The following types of research-based knowledge and research-like activities are included in this course:
Research-based knowledge
  • Classic and basic theory
  • Teacher’s own research
  • Methodology
  • Models
Research-like activities
  • Analysis
  • Discussion, critical reflection, modelling
Description of the teaching methods
The teaching will be a combination of lectures and exercise classes. Additionally there will be video recordings and blended learning activities. During the course there will be 1-2 voluntary home assignments.
Feedback during the teaching period
The lectures include short quizzes and assignments, with answers discussed collectively to reinforce understanding.

Exercise classes focus on solving problems in small groups, fostering constructive dialogue with the lecturer.

Written feedback will be provided on voluntary home assignments.

Students are strongly encouraged to participate actively in all learning activities and to make use of the lecturer’s office hours.
Student workload
Lectures and exercises 32 hours
Exam and exam preparation 30 hours
Preparation 144 hours
Last updated on 26-01-2026