Noisy-OR Models with Latent Confounding

Antti Hyttinen, Frederick Eberhardt, Patrik O. Hoyer
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:411-420, 2011.

Abstract

Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complicated when only one or a few variables are subject to intervention per experiment. For linear causal models with latent variables Hyttinen et al. (2010) gave precise conditions for when such data are sufficient to identify the full model. While their result cannot be extended to discrete-valued variables with arbitrary cause-effect relationships, we show that a similar result can be obtained for the class of causal models whose conditional probability distributions are restricted to a ‘noisy-OR’ parameterization. We further show that identification is preserved under an extension of the model that allows for negative influences, and present learning algorithms that we test for accuracy, scalability and robustness.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-hyttinen11a, title = {Noisy-{OR} Models with Latent Confounding}, author = {Hyttinen, Antti and Eberhardt, Frederick and Hoyer, Patrik O.}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {411--420}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/hyttinen11a/hyttinen11a.pdf}, url = {https://proceedings.mlr.press/r9/hyttinen11a.html}, abstract = {Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complicated when only one or a few variables are subject to intervention per experiment. For linear causal models with latent variables Hyttinen et al. (2010) gave precise conditions for when such data are sufficient to identify the full model. While their result cannot be extended to discrete-valued variables with arbitrary cause-effect relationships, we show that a similar result can be obtained for the class of causal models whose conditional probability distributions are restricted to a ‘noisy-OR’ parameterization. We further show that identification is preserved under an extension of the model that allows for negative influences, and present learning algorithms that we test for accuracy, scalability and robustness.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Noisy-OR Models with Latent Confounding %A Antti Hyttinen %A Frederick Eberhardt %A Patrik O. Hoyer %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-hyttinen11a %I PMLR %P 411--420 %U https://proceedings.mlr.press/r9/hyttinen11a.html %V R9 %X Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complicated when only one or a few variables are subject to intervention per experiment. For linear causal models with latent variables Hyttinen et al. (2010) gave precise conditions for when such data are sufficient to identify the full model. While their result cannot be extended to discrete-valued variables with arbitrary cause-effect relationships, we show that a similar result can be obtained for the class of causal models whose conditional probability distributions are restricted to a ‘noisy-OR’ parameterization. We further show that identification is preserved under an extension of the model that allows for negative influences, and present learning algorithms that we test for accuracy, scalability and robustness. %Z Reissued by PMLR on 04 October 2026.
APA
Hyttinen, A., Eberhardt, F. & Hoyer, P.O.. (2011). Noisy-OR Models with Latent Confounding. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:411-420 Available from https://proceedings.mlr.press/r9/hyttinen11a.html. Reissued by PMLR on 04 October 2026.

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