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Cursus: 202100112
Graphical Models and Causality
Cursus informatieRooster
Studiepunten (ECTS)5
Contactpersoonprof.dr. A.J. Schmidt-Hieber
Contactpersoon van de cursus
prof.dr. A.J. Schmidt-Hieber
prof.dr. A.J. Schmidt-Hieber
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After following this course, the student is able to:
  • explain the strength/weakness behind different approaches for causality
  • propose causal models for data
  • explain and judge the assumptions underlying different approaches
  • do parameter estimation in causal models
  • explain the link between causal models and machine learning
Does smoking cause lung cancer? This has been a highly disputed question in the 50ies when the number of lung cancer deaths surged. In those years the number of smokers increased as well. This suggests a relationship, but this could have been also a pure coincidence. In fact, there were many other possible explanations ranging from car emissions to a genetic disposition that would cause people to be more attracted to smoking and at the same time cause lung cancer. If the latter would be true, prohibiting smoking would not influence the number of lung cancer cases.

So how can we formally establish a causal relationship? The course will cover several concepts of causal relationships and how to infer those from observational data. The theory is applicable to a wide range of applied sciences and is particularly relevant for medical data. In gene studies, for instance, we measure large numbers of variables and typically observe correlations among many of these variables. To find the genetic mechanism behind a disease, this is, however, not enough and we need to uncover the causal pathway.

The course follows the book “Elements of Causal Inference”, see below for the full reference. The material is structured in three main topics: basic principles, bivariate models and multivariate models.
  1. Introduction
    1. Correlation and causation in observational studies
    2. Examples: gene perturbation, pattern recognition
    3. Simple causal models: confounders and colliders
    4. Randomized experiments
  2. Assumptions for causal inference
    1. Independent mechanisms, interventions
    2. Physical structure underlying causal models
  3. Cause‐Effect models
    1. Structural causal models
    2. Counterfactuals
    3. Canonical representation of structural causal models
  4. Learning cause‐effect models
    1. Identifiability, additive noise models
    2. Information theoretic causal inference
    3. Methods for structure identification
    4. Connections to machine learning
  5. Multivariate causal models
    1. graphs
    2. Multivariate structural causal models
    3. Interventions in multivariate causal models
    4. Counterfactuals in multivariate causal models
    5. Markov property, faithfulness and causal minimality
    6. Causal graphical models
    7. Do‐calculus
    8. Equivalence and falsifiability of causal models
  6. Learning multivariate causal models
    1. Identifiability
    2. Additive noise models
    3. Methods for multivariate structure identification
    4. Connection to machine learning
  7. Hidden variables
    1. Interventional sufficiency
    2. Simpson’s paradox
    3. Instrumental variables
    4. Conditional independences and graphical representations
    5. Beyond conditional independence
Students should have solid knowledge of statistics, including knowledge of probability, expectation, mean, variance, discrete and continuous distributions, confidence intervals, simple linear regression. For instance:
‐ Probability Theory (202001344) and Mathematical Statistics (202001348) or
‐ Probability Theory (202001233) and Statistical Techniques (202001033)
Participating study
Master Applied Mathematics
Participating study
Master Computer Science
Participating study
Master Electrical Engineering
Participating study
Master Technical Medicine
Participating study
Master Biomedical Engineering
Participating study
Master Business Information Technology
Verplicht materiaal
Jonas Peters, Dominik Janzing, Bernhard Schölkopf: Elements of Causal Inference, MIT Press, 2017. The book is open access and can be downloaded via‐inference . ISBN 9780262037310.
Aanbevolen materiaal
Steffen Lauritzen: Graphical Models. Oxford University Press, New York NY, 1996. ISBN 0198522193.



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