UvA-DARE ( Digital Academic Repository ) Causal Consistency of Structural Equation Models

By Paul K. Rubenstein, Sebastian Weichwald, Stephan Bongers, Joris M. Mooij, Dominik Janzing, Moritz Grosse-Wentrup, Bernhard Schölkopf. 2017

172 citations recorded by the source corpus.

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 formalise 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 macro-variables are aggregate features of the micro-variables; (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.

Subfields: Artificial Intelligence, Experimental and Cognitive Psychology, Statistics and Probability, Causal Inference & Discovery

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “Deﬁning objects or variables that can be causally related amounts to coarse-graining of more detailed models of the world, including microscopic structural equation models [208], ordinary differential equations [173], [207], and temporally aggregated time series [79].”
Towards Causal Representation Learning (2021, background): “structural equation models [207], ordinary differential equations [173, 208], and temporally aggregated time series [78].”
Causality for Machine Learning (2019, background): “…models in economics, medicine, or psychology uses variables that are abstractions of more elementary concepts, it is challenging to state general conditions under which coarse-grained variables admit causal models with well-defined interventions (Chalupka et al., 2015; Rubenstein et al., 2017).”
On Pearl’s Hierarchy and the Foundations of Causal Inference (2022, background): “It is possible to conceive an SCM as “a high-level abstraction of an underlying system of differen tial equations” [Schölkopf 2019], which under relatively mild conditions is attainable [Rubenstein et al. 2017].”
Algorithmic Recourse: from Counterfactual Explanations to Interventions (2020, background): “Such confounded/correlated interventions, referred to as fat-hand/non-atomic interventions [10], will be explored further in follow-up work, by modelling the world at different causally consistent levels [4, 40].”
Foundations of structural causal models with cycles and latent variables (2016, background): “Previous work has considered interventions only on a specific subset of endogenous variables [2, 3, 62].”
Causal Abstractions of Neural Networks (2021, methodology): “To concretize this, we turn to formal, broadly interventionist theories of causality [25, 19], in which causal processes are characterized by effects of interventions, and theories of abstraction [1, 2, 5, 22] where relationships between two causal processes are determined by the presence of systema”