Counterfactual Transportability: A Formal Approach

Generalizing causal knowledge across environments is a common challenge shared across many of the data-driven disciplines, including AI and ML. Experiments are usually performed in one environment (e.g., in a lab, on Earth, in a training ground), almost invariably, with the intent of being used elsewhere (e.g., outside the lab, on Mars, in the real world), in an environment that is related but somewhat different than the original one, where certain conditions and mechanisms are likely to change. This generalization task has been studied in the causal inference literature under the rubric of transportability (Pearl and Bareinboim, 2011). While most transportability works focused on generalizing associational and interventional distributions, the generalization of counterfactual distributions has not been formally studied. In this paper, we investigate the transportability of counterfactuals from an arbitrary combination of observational and experimental distributions coming from disparate domains. Specifically, we introduce a sufficient and necessary graphical condition and develop an efficient, sound, and complete algorithm for transporting counterfactual quantities across domains in nonparametric settings. Failure of the algorithm implies the impossibility of generalizing the target counterfactual from the available data without further assumptions.