Causal Consistency of Structural Equation Models

Paul K. Rubenstein*, Sebastian Weichwald*, Stephan Bongers, Joris M. Mooij, Dominik Janzing, Moritz Grosse-Wentrup, Bernhard Schoelkopf
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:151-160, 2017.

Abstract

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We for malise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the ‘irrelevant’ or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macrovariables are aggregate features of the microvariables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-rubenstein-17a, title = {Causal Consistency of Structural Equation Models}, author = {Rubenstein*, Paul K. and Weichwald*, Sebastian and Bongers, Stephan and Mooij, Joris M. and Janzing, Dominik and Grosse-Wentrup, Moritz and Schoelkopf, Bernhard}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {151--160}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/rubenstein-17a/rubenstein-17a.pdf}, url = {https://proceedings.mlr.press/r15/rubenstein-17a.html}, abstract = {Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We for malise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the ‘irrelevant’ or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macrovariables are aggregate features of the microvariables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Causal Consistency of Structural Equation Models %A Paul K. Rubenstein* %A Sebastian Weichwald* %A Stephan Bongers %A Joris M. Mooij %A Dominik Janzing %A Moritz Grosse-Wentrup %A Bernhard Schoelkopf %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-rubenstein-17a %I PMLR %P 151--160 %U https://proceedings.mlr.press/r15/rubenstein-17a.html %V R15 %X Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We for malise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the ‘irrelevant’ or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macrovariables are aggregate features of the microvariables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs. %Z Reissued by PMLR on 04 October 2026.
APA
Rubenstein*, P.K., Weichwald*, S., Bongers, S., Mooij, J.M., Janzing, D., Grosse-Wentrup, M. & Schoelkopf, B.. (2017). Causal Consistency of Structural Equation Models. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:151-160 Available from https://proceedings.mlr.press/r15/rubenstein-17a.html. Reissued by PMLR on 04 October 2026.

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