Bayesian Learning, 6 credits

Main field of study

Course level

Advancement level

Course offered for

• Computer Science and Engineering, M Sc in Engineering
• Information Technology, M Sc in Engineering
• Computer Science and Software Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Mathematical analysis; Linear Algebra; Probability and Statistics; Machine Learning; Basic programming.

 

Intended learning outcomes

The course gives a solid introduction to Bayesian learning, with special emphasis on theory, models and methods used in machine learning applications. The student will learn about the basic ideas and concepts in Bayesian analysis from detailed analysis of simple probability models. The course presents simulation algorithms typically used in practical Bayesian work, and course participants will learn how to apply those algorithms to analyze complex machine learning models.
After completing the course the student should be able to:

• derive the posterior distribution for a number of basic probability models
• use simulation algorithms to perform a Bayesian analysis of more complex models
• perform Bayesian prediction and decision making
• perform Bayesian model inference.

Course content

Likelihood, Subjective probability, Bayes theorem, Prior and posterior distribution, Bayesian analysis of the following models: Bernoulli, Normal, Multinomial, Multivariate normal, Linear and nonlinear regression, Binary regression, Mixture models; Regularization priors, Classification, Naïve Bayes, Marginalization, Posterior approximation, Prediction, Decision theory, Markov Chain Monte Carlo, Gibbs sampling, Bayesian variable selection, Model selection, Model averaging.
 

Teaching and working methods

The course consists of lectures, exercises, seminars and computer labs. The lectures introduce concepts and theories that students then use in problem solving at the exercises and computer labs. The seminars are used for student presentations of the computer lab reports and discussions.
 

Examination

Grades

Other information

Supplementary courses:
Advanced Machine Learning, Text Mining, Visual Object Recognition and Detection
 

Department

Director of Studies or equivalent

Examiner

Education components

Course literature

Additional literature

Books

• Gelman, A., Carlin, J.B., Stern, H. S., Dunson, D. B., Vehtari, A., and Donald Rubin, D.B., (2013) Bayesian Data Analysis 3rd edition Chapman & Hall