Counterfactual Fairness under Hidden Confounding

Marc Braun, Jose M. Peña, Adel Daoud
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:92-111, 2026.

Abstract

Designing algorithms that are non-discriminatory has attracted major attention in recent years. It has been shown that a causal perspective is necessary to mitigate unfair discrimination. However, little attention has been paid to how algorithms can make fair decisions under hidden confounding. In this paper, we study counterfactual fairness in the presence of hidden confounding and make two contributions. First, we show that under commonly adopted assumptions, counterfactual fairness is invariant across all causal models consistent with the observed data and causal ordering of the variables. In particular, even in the presence of hidden confounding and non-identifiability of the underlying causal model, all compatible models yield the same counterfactual fairness conclusions. Second, we show how instrumental variables, a tool commonly used in causal inference to address hidden confounding, can help to design fair predictors when the protected attribute is unobserved. Together, our results extend the scope of causal fairness methods to more realistic settings where both confounders and sensitive attributes may be partially or entirely unobserved.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-braun26a, title = {Counterfactual Fairness under Hidden Confounding}, author = {Braun, Marc and Pe{\~n}a, Jose M. and Daoud, Adel}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {92--111}, year = {2026}, editor = {Camps-Valls, Gustau and Leonelli, Manuele and Varando, Gherardo}, volume = {343}, series = {Proceedings of Machine Learning Research}, month = {09--11 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v343/main/assets/braun26a/braun26a.pdf}, url = {https://proceedings.mlr.press/v343/braun26a.html}, abstract = {Designing algorithms that are non-discriminatory has attracted major attention in recent years. It has been shown that a causal perspective is necessary to mitigate unfair discrimination. However, little attention has been paid to how algorithms can make fair decisions under hidden confounding. In this paper, we study counterfactual fairness in the presence of hidden confounding and make two contributions. First, we show that under commonly adopted assumptions, counterfactual fairness is invariant across all causal models consistent with the observed data and causal ordering of the variables. In particular, even in the presence of hidden confounding and non-identifiability of the underlying causal model, all compatible models yield the same counterfactual fairness conclusions. Second, we show how instrumental variables, a tool commonly used in causal inference to address hidden confounding, can help to design fair predictors when the protected attribute is unobserved. Together, our results extend the scope of causal fairness methods to more realistic settings where both confounders and sensitive attributes may be partially or entirely unobserved.} }
Endnote
%0 Conference Paper %T Counterfactual Fairness under Hidden Confounding %A Marc Braun %A Jose M. Peña %A Adel Daoud %B Proceedings of the 13th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2026 %E Gustau Camps-Valls %E Manuele Leonelli %E Gherardo Varando %F pmlr-v343-braun26a %I PMLR %P 92--111 %U https://proceedings.mlr.press/v343/braun26a.html %V 343 %X Designing algorithms that are non-discriminatory has attracted major attention in recent years. It has been shown that a causal perspective is necessary to mitigate unfair discrimination. However, little attention has been paid to how algorithms can make fair decisions under hidden confounding. In this paper, we study counterfactual fairness in the presence of hidden confounding and make two contributions. First, we show that under commonly adopted assumptions, counterfactual fairness is invariant across all causal models consistent with the observed data and causal ordering of the variables. In particular, even in the presence of hidden confounding and non-identifiability of the underlying causal model, all compatible models yield the same counterfactual fairness conclusions. Second, we show how instrumental variables, a tool commonly used in causal inference to address hidden confounding, can help to design fair predictors when the protected attribute is unobserved. Together, our results extend the scope of causal fairness methods to more realistic settings where both confounders and sensitive attributes may be partially or entirely unobserved.
APA
Braun, M., Peña, J.M. & Daoud, A.. (2026). Counterfactual Fairness under Hidden Confounding. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:92-111 Available from https://proceedings.mlr.press/v343/braun26a.html.

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