Causality: fundamental principles and tools

The goal of this chapter is to provide a gentle introduction to Causal Learning (CL), and motivation for its application to medical image analysis, seeking for more robustness against data and domain drifts, and a reliable tool to answer conterfactuals questions and get improved interpretability. The probabilistic formalism at the basis of CL will be introduced, along with basic definitions and assumptions. A number of classical methods to perform causal data analysis (both to establish the causal data generating structure, and to intervene on it) will be illustrated, using simple synthetic datasets. Scaling up to high dimensional and complex data such as medical images is not trivial, and requires the combination of classical CL and modern Deep/Machine Learning techniques: this topic will be further developed in Chapter 17.