Identifiability of Causal Graphs using Functional Models

Jonas Peters, Joris Mooij, Dominik Janzing, Bernhard Schoelkopf
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:655-664, 2011.

Abstract

This work addresses the following question: Under what assumptions on the data generating process can one infer the causal graph from the joint distribution? The approach taken by conditional independence-based causal discovery methods is based on two assumptions: the Markov condition and faithfulness. It has been shown that under these assumptions the causal graph can be identified up to Markov equivalence (some arrows remain undirected) using methods like the PC algorithm. In this work we propose an alternative by defining Identifiable Functional Model Classes (IFMOCs). As our main theorem we prove that if the data generating process belongs to an IFMOC, one can identify the complete causal graph. To the best of our knowledge this is the first identifiability result of this kind that is not limited to linear functional relationships. We discuss how the IFMOC assumption and the Markov and faithfulness assumptions relate to each other and explain why we believe that the IFMOC assumption can be tested more easily on given data. We further provide a practical algorithm that recovers the causal graph from finitely many data; experiments on simulated data support the theoretical findings.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-peters11a, title = {Identifiability of Causal Graphs using Functional Models}, author = {Peters, Jonas and Mooij, Joris and Janzing, Dominik and Schoelkopf, Bernhard}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {655--664}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/peters11a/peters11a.pdf}, url = {https://proceedings.mlr.press/r9/peters11a.html}, abstract = {This work addresses the following question: Under what assumptions on the data generating process can one infer the causal graph from the joint distribution? The approach taken by conditional independence-based causal discovery methods is based on two assumptions: the Markov condition and faithfulness. It has been shown that under these assumptions the causal graph can be identified up to Markov equivalence (some arrows remain undirected) using methods like the PC algorithm. In this work we propose an alternative by defining Identifiable Functional Model Classes (IFMOCs). As our main theorem we prove that if the data generating process belongs to an IFMOC, one can identify the complete causal graph. To the best of our knowledge this is the first identifiability result of this kind that is not limited to linear functional relationships. We discuss how the IFMOC assumption and the Markov and faithfulness assumptions relate to each other and explain why we believe that the IFMOC assumption can be tested more easily on given data. We further provide a practical algorithm that recovers the causal graph from finitely many data; experiments on simulated data support the theoretical findings.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Identifiability of Causal Graphs using Functional Models %A Jonas Peters %A Joris Mooij %A Dominik Janzing %A Bernhard Schoelkopf %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-peters11a %I PMLR %P 655--664 %U https://proceedings.mlr.press/r9/peters11a.html %V R9 %X This work addresses the following question: Under what assumptions on the data generating process can one infer the causal graph from the joint distribution? The approach taken by conditional independence-based causal discovery methods is based on two assumptions: the Markov condition and faithfulness. It has been shown that under these assumptions the causal graph can be identified up to Markov equivalence (some arrows remain undirected) using methods like the PC algorithm. In this work we propose an alternative by defining Identifiable Functional Model Classes (IFMOCs). As our main theorem we prove that if the data generating process belongs to an IFMOC, one can identify the complete causal graph. To the best of our knowledge this is the first identifiability result of this kind that is not limited to linear functional relationships. We discuss how the IFMOC assumption and the Markov and faithfulness assumptions relate to each other and explain why we believe that the IFMOC assumption can be tested more easily on given data. We further provide a practical algorithm that recovers the causal graph from finitely many data; experiments on simulated data support the theoretical findings. %Z Reissued by PMLR on 04 October 2026.
APA
Peters, J., Mooij, J., Janzing, D. & Schoelkopf, B.. (2011). Identifiability of Causal Graphs using Functional Models. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:655-664 Available from https://proceedings.mlr.press/r9/peters11a.html. Reissued by PMLR on 04 October 2026.

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