Aligning Graphical and Functional Causal Abstractions

Willem Schooltink, Fabio Massimo Zennaro
Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:704-730, 2025.

Abstract

Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal abstraction are common in the literature: (i) graphical abstractions, such as Cluster DAGs, which relate models on a structural level, and (ii) functional abstractions, like $\alpha$-abstractions, which relate models by maps between variables and their ranges. In this paper we will align the notions of graphical and functional consistency and show an equivalence between the class of Cluster DAGs, consistent $\alpha$-abstractions, and constructive $\tau$-abstractions. Furthermore, we extend this alignment by introducing more expressive Partial Cluster DAGs. Our results provide a rigorous bridge between the functional and graphical frameworks and allow for adoption and transfer of results between them.

Cite this Paper

BibTeX
@InProceedings{pmlr-v275-schooltink25a, title = {Aligning Graphical and Functional Causal Abstractions}, author = {Schooltink, Willem and Zennaro, Fabio Massimo}, booktitle = {Proceedings of the Fourth Conference on Causal Learning and Reasoning}, pages = {704--730}, year = {2025}, editor = {Huang, Biwei and Drton, Mathias}, volume = {275}, series = {Proceedings of Machine Learning Research}, month = {07--09 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v275/main/assets/schooltink25a/schooltink25a.pdf}, url = {https://proceedings.mlr.press/v275/schooltink25a.html}, abstract = {Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal abstraction are common in the literature: (i) graphical abstractions, such as Cluster DAGs, which relate models on a structural level, and (ii) functional abstractions, like $\alpha$-abstractions, which relate models by maps between variables and their ranges. In this paper we will align the notions of graphical and functional consistency and show an equivalence between the class of Cluster DAGs, consistent $\alpha$-abstractions, and constructive $\tau$-abstractions. Furthermore, we extend this alignment by introducing more expressive Partial Cluster DAGs. Our results provide a rigorous bridge between the functional and graphical frameworks and allow for adoption and transfer of results between them.} }
Endnote
%0 Conference Paper %T Aligning Graphical and Functional Causal Abstractions %A Willem Schooltink %A Fabio Massimo Zennaro %B Proceedings of the Fourth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Biwei Huang %E Mathias Drton %F pmlr-v275-schooltink25a %I PMLR %P 704--730 %U https://proceedings.mlr.press/v275/schooltink25a.html %V 275 %X Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal abstraction are common in the literature: (i) graphical abstractions, such as Cluster DAGs, which relate models on a structural level, and (ii) functional abstractions, like $\alpha$-abstractions, which relate models by maps between variables and their ranges. In this paper we will align the notions of graphical and functional consistency and show an equivalence between the class of Cluster DAGs, consistent $\alpha$-abstractions, and constructive $\tau$-abstractions. Furthermore, we extend this alignment by introducing more expressive Partial Cluster DAGs. Our results provide a rigorous bridge between the functional and graphical frameworks and allow for adoption and transfer of results between them.
APA
Schooltink, W. & Zennaro, F.M.. (2025). Aligning Graphical and Functional Causal Abstractions. Proceedings of the Fourth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 275:704-730 Available from https://proceedings.mlr.press/v275/schooltink25a.html.

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