Georgios-Nikolaos Karelas: Interventions for Identifying Context-Specific Causal Structures
MSc Thesis Presentation
Time: Tue 2021-06-01 11.15
Location: Zoom, meeting ID: 625 8662 8413
Respondent: Georgios-Nikolaos Karelas
The problem of causal discovery is to learn the true causal relations among a system of random variables based on the available data. Learning the true causal structure of p variables can sometimes be difficult, but it is crucial in many fields of science, such as biology, sociology and artificial intelligence. Classically, it is assumed that the true causal relations are completely encoded via a directed acyclic graph (DAG), and there are numerous algorithms for estimating a DAG representative of a causal system from data. Assuming it is feasible, the most effective way of learning the true causal structure is through interventional experiments. Some previous work was made by Eberhardt et al. who identified the sufficient and in the worst case necessary number of interventions needed to learn a DAG, and then studied this problem from a game theoretic perspective, providing an upper bound on the expected number of experiments needed to identify the causal DAG. Here, we consider more general causal models, the CStrees, which allow for the true causal relations to be context-specific. We extend the results of Eberhardt to the family of CStrees by finding the sufficient and in the worst case necessary number of experiments the Scientist must perform in order to discover the true CStree among p variables. We generalize the game theoretic approach presented in Eberhardt's paper, to the CStrees with a specified causal ordering. We also give a geometric description of context-specific hard interventions in CStrees, through a bijection between the stages of the CStree and the faces of a polytope.