From Deterministic ODEs to Dynamic Structural Causal Models

Paul K. Rubenstein, Stephan Bongers, Joris M. Mooij, Bernhard Schoelkopf
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:113-122, 2018.

Abstract

Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the re- lationship between Ordinary Differential Equa- tions and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be mod- elled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-rubenstein18a, title = {From Deterministic ODEs to Dynamic Structural Causal Models}, author = {Rubenstein, Paul K. and Bongers, Stephan and Mooij, Joris M. and Schoelkopf, Bernhard}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {113--122}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/rubenstein18a/rubenstein18a.pdf}, url = {https://proceedings.mlr.press/r16/rubenstein18a.html}, abstract = {Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the re- lationship between Ordinary Differential Equa- tions and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be mod- elled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T From Deterministic ODEs to Dynamic Structural Causal Models %A Paul K. Rubenstein %A Stephan Bongers %A Joris M. Mooij %A Bernhard Schoelkopf %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-rubenstein18a %I PMLR %P 113--122 %U https://proceedings.mlr.press/r16/rubenstein18a.html %V R16 %X Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the re- lationship between Ordinary Differential Equa- tions and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be mod- elled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria. %Z Reissued by PMLR on 04 October 2026.
APA
Rubenstein, P.K., Bongers, S., Mooij, J.M. & Schoelkopf, B.. (2018). From Deterministic ODEs to Dynamic Structural Causal Models. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:113-122 Available from https://proceedings.mlr.press/r16/rubenstein18a.html. Reissued by PMLR on 04 October 2026.

Related Material