Concepts and formal tools for causality studies

In this lecture, basic concepts and formal tools for the study of causality will be introduced and discussed. The focus of the lecture will be on Pearl's causality theory and Shannon's information theory.

The main formal object of Pearl's theory represents the cause-effect relations within a system in terms of arrows between the nodes of a network. Such a network, a so-called Bayesian network, has two components, a structural and a mechanistic one. General measurements in the network can display correlations that do not directly correspond to causal links: "correlation does not imply causation." Reichenbach's common cause principle, on the other hand, refers to an apparently contradicting law. Somewhat simplified, it says that any correlation of variables implies a cause-effect relation or the existence of a common cause of these variables. In this sense, "correlation does imply causation."

In order to disentangle the casual relations that underly correlations, the concept of experimental intervention is required. Pearl's framework allows to formalise this operation in terms of his do-calculus. Surprisingly, actual experimental intervention is not always required in order to identify casual effects. One of the core results of that theory is given in terms of sufficient criteria for the identification of causal effects based on purely observational data. The lecture will highlight the utility of information theory in cases where these criteria are not satisfied. A very general quantitative extension of the common cause principle based on information theory will be presented in this regard.