The causal theory is based upon structural causal models which combine features of the structural equation models (SEM) , the potential-outcome framework of Neyman and Rubin, and the graphical models developed for probabilistic reasoning and causal analysis. In this framework, causal relationships are encoded in a causal graph that incorporates a finite set of nodes and edges representing the involved variables and causal relationships, respectively.
There are two common approaches for learning the causal structures:
- The search-and-score approaches try to find a causal structure by comparing the optimized scores for possible causal structures given the observational data.
- The constraint-based approaches query the observational data for conditional independencies to obtain an undirected skeleton. Building on this skeleton, the algorithms determine the orientation of the detected relationships to construct a causal structure.
When the true causal structure is given, the so-called do-calculus allows for an identification of the causal effects in the observed system. Moreover, the relationships in the causal graph build the basis of estimation procedures to derive the functional relationships that allows to predict the result of an intervention to the system.