Causal Inference by Surrogate Experiments: z-Identifiability

TL;DR

This paper introduces a method for estimating causal effects from surrogate experiments, providing a graphical criterion and an algorithm for z-identifiability, extending do-calculus to more accessible experimental settings.

Contribution

It offers a necessary and sufficient graphical condition and a complete algorithm for z-identifiability, expanding causal inference capabilities beyond traditional interventions.

Findings

Graphical necessary and sufficient condition for z-identifiability

Complete algorithm for computing causal effects from surrogate experiments

Proof of do-calculus completeness relative to z-identifiability

Abstract

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 = empty 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 outcomes). 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.