Identifiability from a Combination of Observations and Experiments

We study the problem of causal identification from an arbitrary collection of observational and experimental distributions, and substantive knowledge about the phenomenon under investigation, which usually comes in the form of a causal graph. We call this problem g-identifiability, or gID for short. In this paper, we introduce a general strategy to prove non-gID based on thickets and hedgelets, which leads to a necessary and sufficient graphical condition for the corresponding decision problem. We further develop a procedure for systematically computing the target effect, and prove that it is sound and complete for gID instances. In other words, the failure of the algorithm in returning an expression implies that the target effect is not computable from the available distributions. Finally, as a corollary of these results, we show that do-calculus is complete for the task of g-identifiability.