We address the problem of transferring causal knowledge learned in one environment to another, potentially different environment, when only limited experiments may be conducted at the source. This generalizes the treatment of transportability introduced in [Pearl and Bareinboim, 2011; Bareinboim and Pearl, 2012b], which deals with transferring causal information when any experiment can be conducted at the source. Given that it is not always feasible to conduct certain controlled experiments, we consider the decision problem whether experiments on a selected subset Z of variables together with qualitative assumptions encoded in a diagram may render causal effects in the target environment computable from the available data. This problem, which we call z-transportability, reduces to ordinary transportability when Z is all-inclusive, and, like the latter, can be given syntactic characterization using the do-calculus [Pearl, 1995; 2000]. This paper establishes a necessary and sufficient condition for causal effects in the target domain to be estimable from both the non-experimental information available and the limited experimental information transferred from the source. We further provides a complete algorithm for computing the transport formula, that is, a way of fusing experimental and observational information to synthesize an unbiased estimate of the desired causal relation.
The study of transportability aims to identify conditions under which causal information learned from experiments can be reused in a different environment where only passive observations can be collected. The theory introduced in [Pearl and Bareinboim, 2011] (henceforth [PB, 2011]) defines formal conditions for such transfer but falls short of providing an effective procedure for deciding, given assumptions about differences between the source and target domains, whether transportability is feasible. This paper provides such procedure. It establishes a necessary and sufficient condition for deciding when causal effects in the target domain are estimable from both the statistical information available and the causal information transferred from the experiments. The paper further provides a complete algorithm for computing the transport formula, that is, a way of fusing experimental and observational information to synthesize an estimate of the desired causal relation.
We study m-transportability, a generalization of transportability, which offers a license to use causal information elicited from experiments and observations in m>=1 source environments to estimate a causal effect in a given targetenvironment. We provide a novel characterization of m-transportability that directly exploits the completeness of do-calculus to obtain the necessary and sufficient conditions for m-transportability. We provide an algorithm for deciding m-transportability that determines whether a causal relation is m-transportable; and if it is, produces a transport formula, that is, a recipe for estimating the desired causal effect by combining experimental information from m source environments with observational information from the target environment.
We address the problem of transferring information learned from experiments to a different environment, in which only passive observations can be collected. We introduce a formal representation called "selection diagrams" for expressing knowledge about differences and commonalities between environments and, using this representation, we derive procedures for deciding whether effects in the target environment can be inferred from experiments conducted elsewhere. When the answer is affirmative, the procedures identify the set of experiments and observations that need be conducted to license the transport. We further discuss how transportability analysis can guide the transfer of knowledge in non-experimental learning to minimize re-measurement cost and improve prediction power.
Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called "transportability", defined as a license to transfer information learned in experimental studies to a different population, on which only observational studies can be conducted. Given a set of assumptions concerning commonalities and differences between the two populations, Pearl and Bareinboim (2011) derived sufficient conditions that permit such transfer to take place. This article summarizes their findings and supplements them with an effective procedure for deciding when and how transportability is feasible. It establishes a necessary and sufficient condition for deciding when causal effects in the target population are estimable from both the statistical information available and the causal information transferred from the experiments. The article further provides a complete algorithm for computing the transport formula, that is, a way of combining observational and experimental information to synthesize bias-free estimate of the desired causal relation. Finally, the article examines the differences between transportability and other variants of generalizability.