Study Guide@lith   Link to LiU Homepage
 

Linköping Institute of Technology

Search

 Link to LiU Homepage
 
Valid for year : 2011
 
TAMS22 Probability Theory and Bayesian Networks, 6 ECTS credits.
/Sannolikhetsteori och bayesianska nätverk/

For:   CS   D   IT   MMAT   Y  

 

Prel. scheduled hours: 48
Rec. self-study hours: 112

  Area of Education: Science

Main field of studies: Mathematics, Applied Mathematics

  Advancement level (G1, G2, A): A

Aim:
The course gives an introduction to the analysis of causal networks. It discusses graphical modelling and algorithms for updating the probability distributions. The student should expect to acquire some basic knowledge of the theory and engineering applications of Bayesian networks. By the end of the course, the student will have:
  • encountered the Bayesian paradigm.
  • seen the definition of a Bayesian Network.
  • seen some applications of Bayesian networks in engineering.
  • understood various graphical representations of conditional independence and how to use them for efficient updating.
  • learned how to construct a junction tree and how to pass messages along a junction tree to update the probability distribution over the network.
  • have encountered Pearl's intervention calculus.
Prerequisites: (valid for students admitted to programmes within which the course is offered)
A first course in probability theory.

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Organisation:
Lectures, tutorials and computer laboratories.

Course contents:
  • Uncertainty and the Bayesian Paradigm, Jeffrey's and Pearl's update methods, multinomial sampling and the Dirichlet distribution.
  • Conditional independence and d-separation, Bayesian Networks.
  • Hard, soft and virtual evidence, Bayesian sufficient statistics, Markov chain Monte Carlo methods
  • Decomposable graphs, junction trees, Markov equivalence, the essential graph and chain graphs.
  • Learning the conditional probability potentials.
  • Learning the graph structure.
  • Parameters and sensitivity; measuring distances between probability distributions.
  • Graphical models and exponential families; conditional Gaussian distributions.
  • Causality and Pearl's intervention calculus.
  • The junction tree and message passing algorithms for probability updating.
  • Factor graphs and the sum product algorithm.


Course literature:
Timo Koski & John Noble: Bayesian Networks: An Introduction, Wiley (required). Timo Koski & John Noble: Bayesian Networks: An Introduction, Wiley (krävs).

Examination:
One written examination
Homework assignments
 5 ECTS
1 ECTS
 


Course language is English.
Department offering the course: MAI.
Director of Studies: Torbjörn Larsson
Examiner: John Noble
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
Link to top of pagep


Contact: TFK , val@tfk.liu.se
Last updated: 01/27/2015