From Ordinary Differential Equations to Structural Causal Models: the deterministic case

Joris Mooij, Dominik Janzing, Bernhard Schoelkopf
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:540-548, 2013.

Abstract

We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-mooij13b, title = {From Ordinary Differential Equations to Structural Causal Models: the deterministic case}, author = {Mooij, Joris and Janzing, Dominik and Schoelkopf, Bernhard}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {540--548}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/mooij13b/mooij13b.pdf}, url = {https://proceedings.mlr.press/r11/mooij13b.html}, abstract = {We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T From Ordinary Differential Equations to Structural Causal Models: the deterministic case %A Joris Mooij %A Dominik Janzing %A Bernhard Schoelkopf %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-mooij13b %I PMLR %P 540--548 %U https://proceedings.mlr.press/r11/mooij13b.html %V R11 %X We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models. %Z Reissued by PMLR on 04 October 2026.
APA
Mooij, J., Janzing, D. & Schoelkopf, B.. (2013). From Ordinary Differential Equations to Structural Causal Models: the deterministic case. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:540-548 Available from https://proceedings.mlr.press/r11/mooij13b.html. Reissued by PMLR on 04 October 2026.

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