Probability Theory and Bayesian Networks, 6 credits

Sannolikhetsteori och bayesianska nätverk, 6 hp

TAMS22

Main field of study

Mathematics Applied Mathematics

Course level

Second cycle

Course type

Programme course

Examiner

Torkel Erhardsson

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV N.B.
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6CDDD Computer Science and Engineering, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6MDAV Computer Science, Master's programme 3 (Autumn 2017) 1 2 English Linköping E
6CITE Information Technology, M Sc in Engineering 7 (Autumn 2017) 1 2 English Linköping E CANCELLED
6MMAT Mathematics, Master's programme 3 (Autumn 2017) 1 2 English Linköping E CANCELLED

Main field of study

Mathematics, Applied Mathematics

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Computer Science and Engineering, M Sc in Engineering
  • Information Technology, M Sc in Engineering
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Mathematics, Master's programme
  • Computer Science, Master's programme

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

A first course in probability theory, a first course in statistics.

Intended learning outcomes

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.

Course content

  • 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.

Teaching and working methods

Lectures and tutorials. Computer assignments as home exercises.

Examination

LAB1Compulsory Assignment1 creditsU, 3, 4, 5
TEN1Written Examination5 creditsU, 3, 4, 5

Grades

Alternative-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Torkel Erhardsson

Course website and other links

http://www.mai.liu.se/~jonob/kurser/TAMS22/

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Course literature

Timo Koski & John Noble: Bayesian Networks: An Introduction, Wiley (krävs).
Code Name Scope Grading scale
LAB1 Compulsory Assignment 1 credits U, 3, 4, 5
TEN1 Written Examination 5 credits U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

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

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
X

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X
X

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X

                            
2.3 System thinking
X
X

                            
2.4 Attitudes, thought, and learning
X

                            
2.5 Ethics, equity, and other responsibilities
X

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X

                            
3.2 Communications
X

                            
3.3 Communication in foreign languages
X

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects
X
X

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects
X
X

                            

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