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FSF3964 Bayesian networks and Causal Inference 7.5 credits

This course is of interest for engineers, statisticians and computer scientists who work with, e.g., modelling of highly complex systems, artificial intelligence and robotics. The course presents Bayesian networks (BNT). A BNT consists of probabilities factorized according to directed acyclic graphs (DAGs). Bayesian networks can be built from human knowledge, or they can be machine-learned from data. Also, due to the DAG structure, Bayesian networks are after machine-learning visually interpretable, therefore promoting human learning and theory building. The course addresses the updating of probabilistic uncertainty in response to evidence, and statistical learning of model parameters and structures. BNTs have probably had their largest impact in artificial intelligence. BNTs allow human learning and machine learning to work in tandem, i.e. BNTs are developed from a combination of human and artificial intelligence. Bayesian networks also have special qualities concerning causality. Causality is central to the understanding and use of data. This is of particular importance when we try to simulate an intervention in a domain, such as estimating the effects of a treatment. In this context, it is imperative to work with a causal model, and Bayesian networks help us make that transition. A fundamental tool of causal inference is so-called intervention calculus and analysis, presented in Pearl et.al. 2016. Theory and methods of causal inference are often shrouded in prohibitive terminology, here we try to make a common sense understanding. Care is given to detailed introduction of the threshold concept of causal parameters by means of counterfactuals.

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FSF3964 (Autumn 2018–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Directed acyclic graphs, and d-separation, conditional independence
  • Markov properties for directed acyclic graphs and faithfulness.
  • Learning about probabilities
  • Structural learning; MDL, predictive inference
  • Exponential familes and graphical models (Conditional Gaussian distributions)
  • Causality and intervention calculus
  • structural causal models, graphical statistical models,
  • the adjustment formula, truncated product formula,
  • the backdoor criterion, front-door criterion.
  • counterfactuals, structural interpretation, axiomatics of counterfactuals, probabilities of counterfactuals, Three interpretations of probability of causation and counterfactuals.

Intended learning outcomes

To pass the course, the student:

  • will be able to assess when to use a Bayesian network as a model for an interaction of several variables.
  • will be able to identify statements of conditional independence by a DAG.
  • will be able to use at least two algorithms to learn the structure of a Bayesian network from data
  • will be able to use available software for update of probabilities
  • will be able to recognize a situation, where causal inference is required
  • will be able to apply intervention calculus
  • will be able to identify causal parameters,
  • will be able to find the scientific conditions when it is possible to estimate causal parameters from data
  • knows the main interpretations counterfactuals and their equivalence
  • can place causal inference in the general picture of statistical learning theory
  • can present clearly a topic in causal inference

Literature and preparations

Specific prerequisites

First or second cycle courses in probability, in differential and integral calculus.
Recommended: FSF3961 Statistical inference, SF2955 Statistical learning, SF2740 Graph theory.

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

• T. Koski & J.Noble: Bayesian Networks and Causal Probability Calculus. 2009.Bayesian Networks: An Introduction.  J.Wiley & Sons 2009.  ISBN : 978-0-470-74304-1 Press, 2015, ISBN 978-1-107-06507-9
• Adnan Darwiche: Modeling and reasoning with Bayesian networks. 2009, Cambridge University Press ISBN: 0-521-88438-1 (hardback)
• David Poole & Alan Mackworth:  Artificial Intelligence: Foundations of Computational Agents.  Cambridge University Press, 2010.  Online ISBN 9780511794797
• S.L. Morgan & C.Winship: Counterfactuals and causal inference. 2nd Edition. Cambridge Univ. 
• J.Pearl, M. Glymour & N.P: Jewell: Causal inference in statistics. A Primer. J.Wiley & Sons 2016, ISBN: 9781119186847  

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F

Examination

  • HEM1 - Homework assignments, 7.5 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examination is computer homework project, homework assignments and presentations

Other requirements for final grade

Accept Homework assignments

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

No information inserted

Contact

Timo Koski (tjtkoski@kth.se)

Postgraduate course

Postgraduate courses at SCI/Mathematics