Bounding Counterfactuals under Selection Bias

Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas, David Huber, Dario Azzimonti
Proceedings of The 11th International Conference on Probabilistic Graphical Models, PMLR 186:289-300, 2022.

Abstract

Causal analysis may be affected by selection bias, which is defined as the systematic exclusion of data from a certain subpopulation. Previous work in this area focused on the derivation of identifiability conditions. We propose instead a first algorithm to address both identifiable and unidentifiable queries. We prove that, in spite of the missingness induced by the selection bias, the likelihood of the available data is unimodal. This enables us to use the causal expectation-maximisation scheme to obtain the values of causal queries in the identifiable case, and to compute bounds otherwise. Experiments demonstrate the approach to be practically viable. Theoretical convergence characterisations are provided.

Cite this Paper

BibTeX
@InProceedings{pmlr-v186-zaffalon22a, title = {Bounding Counterfactuals under Selection Bias}, author = {Zaffalon, Marco and Antonucci, Alessandro and Caba{\~n}as, Rafael and Huber, David and Azzimonti, Dario}, booktitle = {Proceedings of The 11th International Conference on Probabilistic Graphical Models}, pages = {289--300}, year = {2022}, editor = {Salmerón, Antonio and Rumı́, Rafael}, volume = {186}, series = {Proceedings of Machine Learning Research}, month = {05--07 Oct}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v186/zaffalon22a/zaffalon22a.pdf}, url = {https://proceedings.mlr.press/v186/zaffalon22a.html}, abstract = {Causal analysis may be affected by selection bias, which is defined as the systematic exclusion of data from a certain subpopulation. Previous work in this area focused on the derivation of identifiability conditions. We propose instead a first algorithm to address both identifiable and unidentifiable queries. We prove that, in spite of the missingness induced by the selection bias, the likelihood of the available data is unimodal. This enables us to use the causal expectation-maximisation scheme to obtain the values of causal queries in the identifiable case, and to compute bounds otherwise. Experiments demonstrate the approach to be practically viable. Theoretical convergence characterisations are provided.} }
Endnote
%0 Conference Paper %T Bounding Counterfactuals under Selection Bias %A Marco Zaffalon %A Alessandro Antonucci %A Rafael Cabañas %A David Huber %A Dario Azzimonti %B Proceedings of The 11th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2022 %E Antonio Salmerón %E Rafael Rumı́ %F pmlr-v186-zaffalon22a %I PMLR %P 289--300 %U https://proceedings.mlr.press/v186/zaffalon22a.html %V 186 %X Causal analysis may be affected by selection bias, which is defined as the systematic exclusion of data from a certain subpopulation. Previous work in this area focused on the derivation of identifiability conditions. We propose instead a first algorithm to address both identifiable and unidentifiable queries. We prove that, in spite of the missingness induced by the selection bias, the likelihood of the available data is unimodal. This enables us to use the causal expectation-maximisation scheme to obtain the values of causal queries in the identifiable case, and to compute bounds otherwise. Experiments demonstrate the approach to be practically viable. Theoretical convergence characterisations are provided.
APA
Zaffalon, M., Antonucci, A., Cabañas, R., Huber, D. & Azzimonti, D.. (2022). Bounding Counterfactuals under Selection Bias. Proceedings of The 11th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 186:289-300 Available from https://proceedings.mlr.press/v186/zaffalon22a.html.

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