Representation of context-specific causal models with observational and interventional data

We address the problem of representing context-specific causal models based on both observational and experimental data collected under general (e.g. hard or soft) interventions by introducing a new family of context-specific conditional independence models called CStrees. This family is defined via a novel factorization criterion that allows for a generalization of the factorization property defining general interventional directed acyclic graph (DAG) models. We derive a graphical characterization of model equivalence for observational CStrees that extends the Verma and Pearl criterion for DAGs. This characterization is then extended to CStree models under general, context-specific interventions. To obtain these results, we formalize a notion of context-specific intervention that can be incorporated into concise graphical representations of CStree models. We relate CStrees to other context-specific models, showing that the families of DAGs, CStrees, labelled DAGs, and staged trees form a strict chain of inclusions. We then present an algorithm for learning CStrees from a combination of observational and interventional data where the intervention targets are assumed to be unknown with hard or soft and possibly context-specific effects. The algorithm, evaluated on simulated and real data, performs well in the recovery of context-specific dependence structure as well as context-specific interventional perturbations.