Structural Causal Models Are (Solvable by) Credal Networks

Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas
Proceedings of the 10th International Conference on Probabilistic Graphical Models, PMLR 138:581-592, 2020.

Abstract

A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal model into a credal network. Causal inferences, such as interventions and counterfactuals, can consequently be obtained by standard algorithms for the updating of credal nets. These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries. A characterization of the causal models that allow the map above to be compactly derived is given, along with a discussion about the scalability for general models. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks and hence to systematically compute causal inferences. A number of demonstrative examples is presented to clarify our methodology. Extensive experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v138-zaffalon20a, title = {Structural Causal Models Are (Solvable by) Credal Networks}, author = {Zaffalon, Marco and Antonucci, Alessandro and Caba\~nas, Rafael}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models}, pages = {581--592}, year = {2020}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, volume = {138}, series = {Proceedings of Machine Learning Research}, month = {23--25 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v138/zaffalon20a/zaffalon20a.pdf}, url = {https://proceedings.mlr.press/v138/zaffalon20a.html}, abstract = {A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal model into a credal network. Causal inferences, such as interventions and counterfactuals, can consequently be obtained by standard algorithms for the updating of credal nets. These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries. A characterization of the causal models that allow the map above to be compactly derived is given, along with a discussion about the scalability for general models. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks and hence to systematically compute causal inferences. A number of demonstrative examples is presented to clarify our methodology. Extensive experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.} }
Endnote
%0 Conference Paper %T Structural Causal Models Are (Solvable by) Credal Networks %A Marco Zaffalon %A Alessandro Antonucci %A Rafael Cabañas %B Proceedings of the 10th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2020 %E Manfred Jaeger %E Thomas Dyhre Nielsen %F pmlr-v138-zaffalon20a %I PMLR %P 581--592 %U https://proceedings.mlr.press/v138/zaffalon20a.html %V 138 %X A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal model into a credal network. Causal inferences, such as interventions and counterfactuals, can consequently be obtained by standard algorithms for the updating of credal nets. These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries. A characterization of the causal models that allow the map above to be compactly derived is given, along with a discussion about the scalability for general models. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks and hence to systematically compute causal inferences. A number of demonstrative examples is presented to clarify our methodology. Extensive experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.
APA
Zaffalon, M., Antonucci, A. & Cabañas, R.. (2020). Structural Causal Models Are (Solvable by) Credal Networks. Proceedings of the 10th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 138:581-592 Available from https://proceedings.mlr.press/v138/zaffalon20a.html.

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