Identifying confounders using additive noise models

Dominik Janzing, Jonas Peters, Joris Mooij, Bernhard Schoelkopf
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:249-257, 2009.

Abstract

We propose a method for inferring the existence of a latent common cause (’confounder’) of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joint distribution of the effects. We state and prove a theoretical result that provides evidence for the conjecture that the model is generically identifiable under suitable technical conditions. In addition, we propose a practical method to estimate the confounder from a finite i.i.d. sample of the effects and illustrate that the method works well on both simulated and real-world data.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-janzing09a, title = {Identifying confounders using additive noise models}, author = {Janzing, Dominik and Peters, Jonas and Mooij, Joris and Schoelkopf, Bernhard}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {249--257}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/janzing09a/janzing09a.pdf}, url = {https://proceedings.mlr.press/r7/janzing09a.html}, abstract = {We propose a method for inferring the existence of a latent common cause (’confounder’) of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joint distribution of the effects. We state and prove a theoretical result that provides evidence for the conjecture that the model is generically identifiable under suitable technical conditions. In addition, we propose a practical method to estimate the confounder from a finite i.i.d. sample of the effects and illustrate that the method works well on both simulated and real-world data.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Identifying confounders using additive noise models %A Dominik Janzing %A Jonas Peters %A Joris Mooij %A Bernhard Schoelkopf %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-janzing09a %I PMLR %P 249--257 %U https://proceedings.mlr.press/r7/janzing09a.html %V R7 %X We propose a method for inferring the existence of a latent common cause (’confounder’) of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joint distribution of the effects. We state and prove a theoretical result that provides evidence for the conjecture that the model is generically identifiable under suitable technical conditions. In addition, we propose a practical method to estimate the confounder from a finite i.i.d. sample of the effects and illustrate that the method works well on both simulated and real-world data. %Z Reissued by PMLR on 04 October 2026.
APA
Janzing, D., Peters, J., Mooij, J. & Schoelkopf, B.. (2009). Identifying confounders using additive noise models. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:249-257 Available from https://proceedings.mlr.press/r7/janzing09a.html. Reissued by PMLR on 04 October 2026.

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