Causal Inference by Surrogate Experiments: z-Identifiability

Elias Bareinboim, Judea Pearl
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:111-118, 2012.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-bareinboim12a, title = {Causal Inference by Surrogate Experiments: z-Identifiability}, author = {Bareinboim, Elias and Pearl, Judea}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {111--118}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/bareinboim12a/bareinboim12a.pdf}, url = {https://proceedings.mlr.press/r10/bareinboim12a.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Causal Inference by Surrogate Experiments: z-Identifiability %A Elias Bareinboim %A Judea Pearl %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-bareinboim12a %I PMLR %P 111--118 %U https://proceedings.mlr.press/r10/bareinboim12a.html %V R10 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Bareinboim, E. & Pearl, J.. (2012). Causal Inference by Surrogate Experiments: z-Identifiability. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:111-118 Available from https://proceedings.mlr.press/r10/bareinboim12a.html. Reissued by PMLR on 04 October 2026.

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