Causal Optimal Transport of Abstractions

Yorgos Felekis, Fabio Massimo Zennaro, Nicola Branchini, Theodoros Damoulas
Proceedings of the Third Conference on Causal Learning and Reasoning, PMLR 236:462-498, 2024.

Abstract

Causal abstraction (CA) theory establishes formal criteria for relating multiple structural causal models (SCMs) at different levels of granularity by defining maps between them. These maps have significant relevance for real-world challenges such as synthesizing causal evidence from multiple experimental environments, learning causally consistent representations at different resolutions, and linking interventions across multiple SCMs. In this work, we propose COTA, the first method to learn abstraction maps from observational and interventional data without assuming complete knowledge of the underlying SCMs. In particular, we introduce a multi-marginal Optimal Transport (OT) formulation that enforces do-calculus causal constraints, together with a cost function that relies on interventional information. We extensively evaluate COTA on synthetic and real world problems, and showcase its advantages over non-causal, independent and aggregated OT formulations. Finally, we demonstrate the efficiency of our method as a data augmentation tool by comparing it against prior art of CA learning, which assumes fully specified SCMs, on a real-world downstream task.

Cite this Paper

BibTeX
@InProceedings{pmlr-v236-felekis24a, title = {Causal Optimal Transport of Abstractions}, author = {Felekis, Yorgos and Zennaro, Fabio Massimo and Branchini, Nicola and Damoulas, Theodoros}, booktitle = {Proceedings of the Third Conference on Causal Learning and Reasoning}, pages = {462--498}, year = {2024}, editor = {Locatello, Francesco and Didelez, Vanessa}, volume = {236}, series = {Proceedings of Machine Learning Research}, month = {01--03 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v236/felekis24a/felekis24a.pdf}, url = {https://proceedings.mlr.press/v236/felekis24a.html}, abstract = {Causal abstraction (CA) theory establishes formal criteria for relating multiple structural causal models (SCMs) at different levels of granularity by defining maps between them. These maps have significant relevance for real-world challenges such as synthesizing causal evidence from multiple experimental environments, learning causally consistent representations at different resolutions, and linking interventions across multiple SCMs. In this work, we propose COTA, the first method to learn abstraction maps from observational and interventional data without assuming complete knowledge of the underlying SCMs. In particular, we introduce a multi-marginal Optimal Transport (OT) formulation that enforces do-calculus causal constraints, together with a cost function that relies on interventional information. We extensively evaluate COTA on synthetic and real world problems, and showcase its advantages over non-causal, independent and aggregated OT formulations. Finally, we demonstrate the efficiency of our method as a data augmentation tool by comparing it against prior art of CA learning, which assumes fully specified SCMs, on a real-world downstream task.} }
Endnote
%0 Conference Paper %T Causal Optimal Transport of Abstractions %A Yorgos Felekis %A Fabio Massimo Zennaro %A Nicola Branchini %A Theodoros Damoulas %B Proceedings of the Third Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2024 %E Francesco Locatello %E Vanessa Didelez %F pmlr-v236-felekis24a %I PMLR %P 462--498 %U https://proceedings.mlr.press/v236/felekis24a.html %V 236 %X Causal abstraction (CA) theory establishes formal criteria for relating multiple structural causal models (SCMs) at different levels of granularity by defining maps between them. These maps have significant relevance for real-world challenges such as synthesizing causal evidence from multiple experimental environments, learning causally consistent representations at different resolutions, and linking interventions across multiple SCMs. In this work, we propose COTA, the first method to learn abstraction maps from observational and interventional data without assuming complete knowledge of the underlying SCMs. In particular, we introduce a multi-marginal Optimal Transport (OT) formulation that enforces do-calculus causal constraints, together with a cost function that relies on interventional information. We extensively evaluate COTA on synthetic and real world problems, and showcase its advantages over non-causal, independent and aggregated OT formulations. Finally, we demonstrate the efficiency of our method as a data augmentation tool by comparing it against prior art of CA learning, which assumes fully specified SCMs, on a real-world downstream task.
APA
Felekis, Y., Zennaro, F.M., Branchini, N. & Damoulas, T.. (2024). Causal Optimal Transport of Abstractions. Proceedings of the Third Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 236:462-498 Available from https://proceedings.mlr.press/v236/felekis24a.html.

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