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 an- other in the sense that they agree in their pre- dictions of the effects of interventions. We for- malise this notion of consistency in the case of Structural Equation Models (SEMs) by intro- ducing 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 macro- variables are aggregate features of the micro- variables; (c) dynamical time series models ver- sus models of their stationary behaviour. Our analysis stresses the importance of well speci- fied interventions in the causal modelling pro- cess 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 an- other in the sense that they agree in their pre- dictions of the effects of interventions. We for- malise this notion of consistency in the case of Structural Equation Models (SEMs) by intro- ducing 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 macro- variables are aggregate features of the micro- variables; (c) dynamical time series models ver- sus models of their stationary behaviour. Our analysis stresses the importance of well speci- fied interventions in the causal modelling pro- cess 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 an- other in the sense that they agree in their pre- dictions of the effects of interventions. We for- malise this notion of consistency in the case of Structural Equation Models (SEMs) by intro- ducing 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 macro- variables are aggregate features of the micro- variables; (c) dynamical time series models ver- sus models of their stationary behaviour. Our analysis stresses the importance of well speci- fied interventions in the causal modelling pro- cess 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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