
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.
 Introduction
 Correlation and causation in observational studies
 Examples: gene perturbation, pattern recognition
 Simple causal models: confounders and colliders
 Randomized experiments
 Assumptions for causal inference
 Independent mechanisms, interventions
 Physical structure underlying causal models
 Cause‐Effect models
 Structural causal models
 Counterfactuals
 Canonical representation of structural causal models
 Learning cause‐effect models
 Identifiability, additive noise models
 Information theoretic causal inference
 Methods for structure identification
 Connections to machine learning
 Multivariate causal models
 graphs
 Multivariate structural causal models
 Interventions in multivariate causal models
 Counterfactuals in multivariate causal models
 Markov property, faithfulness and causal minimality
 Causal graphical models
 Do‐calculus
 Equivalence and falsifiability of causal models
 Learning multivariate causal models
 Identifiability
 Additive noise models
 Methods for multivariate structure identification
 Connection to machine learning
 Hidden variables
 Interventional sufficiency
 Simpson’s paradox
 Instrumental variables
 Conditional independences and graphical representations
 Beyond conditional independence




 VoorkennisStudents 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) 
Master Applied Mathematics 
Master Electrical Engineering 
Master Technical Medicine 
Master Biomedical Engineering 
Master Business Information Technology 
  Verplicht materiaalBookJonas Peters, Dominik Janzing,
Bernhard Schölkopf: Elements of Causal
Inference, MIT Press, 2017. The book is open access and can be downloaded
via https://mitpress.mit.edu/books/elementscausal‐inference . ISBN 9780262037310. 

 Aanbevolen materiaalBookSteffen Lauritzen: Graphical Models. Oxford University Press, New York NY, 1996. ISBN 0198522193. 

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