Causal Inference - Interactive curriculae of TU Ilmenau

fundamentals of analysis, linear algebra, probability theory, Python programming or Matlab programming

Upon completion of this course, students are able to comprehensively grasp the fundamentals of Causal Discovery. They are capable of constructing Structural Causal Models and identifying the necessary properties for deriving causal relationships. Additionally, students are empowered to independently implement common algorithms in the field of causal inference, such as DAG enumeration, SGS, and the PC algorithm, and apply them to real-world data, such as climate time series. Thus, this course provides a solid foundation for independent research in the field of causal inference.

In the beginning, we will motivate the relevance of this type of inference and explore its extent in terms of application areas. Next, we will discuss the development of formal definitions of causality over time and delve into the general history of causality. To establish a foundation for the crucial components necessary for later algorithms, we will first recap concepts from probability theory. Following that, we will introduce Graphs, Bayesian Networks, and Structural Causal Models.
As testing is a key part, we will have a statistics interlude covering Conditional Independence Testing. Subsequently, causal discovery and the corresponding assumptions, such as acyclicity, causal Markov condition, faithfulness, and causal sufficiency, will be introduced. Then, algorithms such as DAG enumeration, SGS, and the PC algorithm will be discussed, along with their extensions to time-series, such as PCMCI and derivatives.
Depending on the course's progress, we will also explore aspects such as Causal Effect Estimation, Causal Effect Identification, and Restricted Structural Causal Models. The course will conclude with a discussion on latent variables and algorithms to address their existence.

Projector, assignments, slides, jupyter notebooks, personal computer with Python or Matlab to work on the programming part of the exercises

Pearl, Judea. 2000. Causality: Models, Reasoning, and Inference. New York, NY: Cambridge University Press.


Spirtes, P., C. Glymour, and R. Scheines. 2000. Causation, Prediction, and Search. Boston: MIT Press.

Pearl, Judea. 2009. Causal Inference in Statistics: An Overview. Statistics Surveys 3: 96–146. https://doi.org/10.1214/09-SS057. 


Peters, Jonas, Dominik Janzing, and Bernhard Schölkopf. 2017. Elements of Causal Inference: Foundations and Learning Algorithms. Cambridge, MA: MIT Press.