Two Optimal Strategies for Active Learning of Causal Models from Interventions

From observational data alone, a causal DAG is in general only identifiable up to Markov equivalence. Interventional data generally improves identifiability; however, the gain of an intervention strongly depends on the intervention target, i.e., the intervened variables. We present active learning strategies calculating optimal interventions for two different learning goals. The first one is a greedy approach using single-vertex interventions that maximizes the number of edges that can be oriented after each intervention. The second one yields in polynomial time a minimum set of targets of arbitrary size that guarantees full identifiability. This second approach proves a conjecture of Eberhardt (2008) indicating the number of unbounded intervention targets which is sufficient and in the worst case necessary for full identifiability. We compare our two active learning approaches to random interventions in a simulation study.