Stability of Causal Inference

Leonard Schulman California Institute of Technology, Piyush Srivastava California Institute of Techno
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:552-561, 2016.

Abstract

?We consider the sensitivity of causal identification to small perturbations in the input. A long line of work culminating in papers by Shpitser and Pearl and Huang and Valtorta led to a complete procedure for the causal identification problem. In our main result in this paper, we show that the identification function computed by these procedures is in some cases extremely unstable numerically. Specifically, the "condition number" of causal identification can be of the order of ?(exp(n^{0.49})) on an identifiable semi-Markovian model with n visible nodes. That is, in order to give an output accurate to d bits, the empirical probabilities of the observable events need to be obtained to accuracy d+?(n^{0.49}) bits.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-technology16a, title = {Stability of Causal Inference}, author = {Technology, Leonard Schulman California Institute of and Techno, Piyush Srivastava California Institute of}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {552--561}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/technology16a/technology16a.pdf}, url = {https://proceedings.mlr.press/r14/technology16a.html}, abstract = {?We consider the sensitivity of causal identification to small perturbations in the input. A long line of work culminating in papers by Shpitser and Pearl and Huang and Valtorta led to a complete procedure for the causal identification problem. In our main result in this paper, we show that the identification function computed by these procedures is in some cases extremely unstable numerically. Specifically, the "condition number" of causal identification can be of the order of ?(exp(n^{0.49})) on an identifiable semi-Markovian model with n visible nodes. That is, in order to give an output accurate to d bits, the empirical probabilities of the observable events need to be obtained to accuracy d+?(n^{0.49}) bits.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Stability of Causal Inference %A Leonard Schulman California Institute of Technology %A Piyush Srivastava California Institute of Techno %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-technology16a %I PMLR %P 552--561 %U https://proceedings.mlr.press/r14/technology16a.html %V R14 %X ?We consider the sensitivity of causal identification to small perturbations in the input. A long line of work culminating in papers by Shpitser and Pearl and Huang and Valtorta led to a complete procedure for the causal identification problem. In our main result in this paper, we show that the identification function computed by these procedures is in some cases extremely unstable numerically. Specifically, the "condition number" of causal identification can be of the order of ?(exp(n^{0.49})) on an identifiable semi-Markovian model with n visible nodes. That is, in order to give an output accurate to d bits, the empirical probabilities of the observable events need to be obtained to accuracy d+?(n^{0.49}) bits. %Z Reissued by PMLR on 04 October 2026.
APA
Technology, L.S.C.I.o. & Techno, P.S.C.I.o.. (2016). Stability of Causal Inference. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:552-561 Available from https://proceedings.mlr.press/r14/technology16a.html. Reissued by PMLR on 04 October 2026.

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