Learning Bivariate Functional Causal Models

Finding the causal direction in the cause-effect pair problem has been addressed in the literature by comparing two alternative generative models X → Y and Y → X. In this chapter, we first define what is meant by generative modeling and what are the main assumptions usually invoked in the literature in this bivariate setting. Then we present the theoretical identifiability problem that arises when considering causal graph with only two variables. It will lead us to present the general ideas used in the literature to perform a model selection based on the evaluation of a complexity/fit trade-off. Three main families of methods can be identified: methods making restrictive assumptions on the class of admissible causal mechanism, methods computing a smooth trade-off between fit and complexity and methods exploiting independence between cause and mechanism.