Confounding Equivalence in Causal Inference

Judea Pearl; Azaria Paz

Confounding Equivalence in Causal Inference

Judea Pearl, Azaria Paz

Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:432-440, 2010.

Abstract

The paper provides a simple test for deciding, from a given causal diagram, whether two sets of variables have the same bias-reducing potential under adjustment. The test re- quires that one of the following two condi- tions holds: either (1) both sets are admis- sible (i.e., satisfy the back-door criterion) or (2) the Markov boundaries surrounding the manipulated variable(s) are identical in both sets. Applications to covariate selection and model testing are discussed.

Cite this Paper

BibTeX

@InProceedings{pmlr-vR8-pearl10c,
  title = 	 {Confounding Equivalence in Causal Inference},
  author =       {Pearl, Judea and Paz, Azaria},
  booktitle = 	 {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence},
  pages = 	 {432--440},
  year = 	 {2010},
  editor = 	 {Grünwald, Peter and Spirtes, Peter},
  volume = 	 {R8},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {08--11 Jul},
  publisher =    {PMLR},
  pdf = 	 {https://raw.githubusercontent.com/mlresearch/r8/main/assets/pearl10c/pearl10c.pdf},
  url = 	 {https://proceedings.mlr.press/r8/pearl10c.html},
  abstract = 	 {The paper provides a simple test for deciding, from a given causal diagram, whether two sets of variables have the same bias-reducing potential under adjustment. The test re- quires that one of the following two condi- tions holds: either (1) both sets are admis- sible (i.e., satisfy the back-door criterion) or (2) the Markov boundaries surrounding the manipulated variable(s) are identical in both sets. Applications to covariate selection and model testing are discussed.},
  note =         {Reissued by PMLR on 04 October 2026.}
}

Endnote

%0 Conference Paper
%T Confounding Equivalence in Causal Inference
%A Judea Pearl
%A Azaria Paz
%B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence
%C Proceedings of Machine Learning Research
%D 2010
%E Peter Grünwald
%E Peter Spirtes	
%F pmlr-vR8-pearl10c
%I PMLR
%P 432--440
%U https://proceedings.mlr.press/r8/pearl10c.html
%V R8
%X The paper provides a simple test for deciding, from a given causal diagram, whether two sets of variables have the same bias-reducing potential under adjustment. The test re- quires that one of the following two condi- tions holds: either (1) both sets are admis- sible (i.e., satisfy the back-door criterion) or (2) the Markov boundaries surrounding the manipulated variable(s) are identical in both sets. Applications to covariate selection and model testing are discussed.
%Z Reissued by PMLR on 04 October 2026.

APA

Pearl, J. & Paz, A.. (2010). Confounding Equivalence in Causal Inference. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:432-440 Available from https://proceedings.mlr.press/r8/pearl10c.html. Reissued by PMLR on 04 October 2026.

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