Causal Abstraction Learning based on the Semantic Embedding Principle

Gabriele D’Acunto, Fabio Massimo Zennaro, Yorgos Felekis, Paolo Di Lorenzo
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:11776-11812, 2025.

Abstract

Structural causal models (SCMs) allow us to investigate complex systems at multiple levels of resolution. The causal abstraction (CA) framework formalizes the mapping between high- and low-level SCMs. We address CA learning in a challenging and realistic setting, where SCMs are inaccessible, interventional data is unavailable, and sample data is misaligned. A key principle of our framework is semantic embedding, formalized as the high-level distribution lying on a subspace of the low-level one. This principle naturally links linear CA to the geometry of the Stiefel manifold. We present a category-theoretic approach to SCMs that enables the learning of a CA by finding a morphism between the low- and high-level probability measures, adhering to the semantic embedding principle. Consequently, we formulate a general CA learning problem. As an application, we solve the latter problem for linear CA; considering Gaussian measures and the Kullback-Leibler divergence as an objective. Given the nonconvexity of the learning task, we develop three algorithms building upon existing paradigms for Riemannian optimization. We demonstrate that the proposed methods succeed on both synthetic and real-world brain data with different degrees of prior information about the structure of CA.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-d-acunto25a, title = {Causal Abstraction Learning based on the Semantic Embedding Principle}, author = {D'Acunto, Gabriele and Zennaro, Fabio Massimo and Felekis, Yorgos and Di Lorenzo, Paolo}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {11776--11812}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/d-acunto25a/d-acunto25a.pdf}, url = {https://proceedings.mlr.press/v267/d-acunto25a.html}, abstract = {Structural causal models (SCMs) allow us to investigate complex systems at multiple levels of resolution. The causal abstraction (CA) framework formalizes the mapping between high- and low-level SCMs. We address CA learning in a challenging and realistic setting, where SCMs are inaccessible, interventional data is unavailable, and sample data is misaligned. A key principle of our framework is semantic embedding, formalized as the high-level distribution lying on a subspace of the low-level one. This principle naturally links linear CA to the geometry of the Stiefel manifold. We present a category-theoretic approach to SCMs that enables the learning of a CA by finding a morphism between the low- and high-level probability measures, adhering to the semantic embedding principle. Consequently, we formulate a general CA learning problem. As an application, we solve the latter problem for linear CA; considering Gaussian measures and the Kullback-Leibler divergence as an objective. Given the nonconvexity of the learning task, we develop three algorithms building upon existing paradigms for Riemannian optimization. We demonstrate that the proposed methods succeed on both synthetic and real-world brain data with different degrees of prior information about the structure of CA.} }
Endnote
%0 Conference Paper %T Causal Abstraction Learning based on the Semantic Embedding Principle %A Gabriele D’Acunto %A Fabio Massimo Zennaro %A Yorgos Felekis %A Paolo Di Lorenzo %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-d-acunto25a %I PMLR %P 11776--11812 %U https://proceedings.mlr.press/v267/d-acunto25a.html %V 267 %X Structural causal models (SCMs) allow us to investigate complex systems at multiple levels of resolution. The causal abstraction (CA) framework formalizes the mapping between high- and low-level SCMs. We address CA learning in a challenging and realistic setting, where SCMs are inaccessible, interventional data is unavailable, and sample data is misaligned. A key principle of our framework is semantic embedding, formalized as the high-level distribution lying on a subspace of the low-level one. This principle naturally links linear CA to the geometry of the Stiefel manifold. We present a category-theoretic approach to SCMs that enables the learning of a CA by finding a morphism between the low- and high-level probability measures, adhering to the semantic embedding principle. Consequently, we formulate a general CA learning problem. As an application, we solve the latter problem for linear CA; considering Gaussian measures and the Kullback-Leibler divergence as an objective. Given the nonconvexity of the learning task, we develop three algorithms building upon existing paradigms for Riemannian optimization. We demonstrate that the proposed methods succeed on both synthetic and real-world brain data with different degrees of prior information about the structure of CA.
APA
D’Acunto, G., Zennaro, F.M., Felekis, Y. & Di Lorenzo, P.. (2025). Causal Abstraction Learning based on the Semantic Embedding Principle. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:11776-11812 Available from https://proceedings.mlr.press/v267/d-acunto25a.html.

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