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Causal Inference by Surrogate Experiments: z-Identifiability
CALIFORNIA UNIV LOS ANGELES COGNITIVE SYSTEMS LAB
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We address the problem of estimating the effect of intervening on a set of variables X from experiments on a different set, Z, that is more accessible to manipulation. This problem, which we call z-identifiability reduces to ordinary identifiability when Z phi and like the latter, can be given syntactic characterization using the do-calculus Pearl, 1995 2000. We provide a graphical necessary and sufficient condition for z- identifiability for arbitrary sets X,Z, and Y the out- comes. We further develop a complete algorithm for computing the causal effect of X on Y using information provided by experiments on Z. Finally, we use our results to prove completeness of do-calculus relative to z-identifiability, a result that does not follow from completeness relative to ordinary identifiability.
APPROVED FOR PUBLIC RELEASE