Causal Modeling With Infinitely Many Variables
This work addresses a foundational limitation in causal modeling for fields like dynamical systems, though it appears incremental as it builds directly on existing SEM frameworks.
The paper tackles the problem of extending structural-equations models (SEMs) to handle infinitely many variables, which is necessary for modeling dynamical systems, by introducing generalized SEMs (GSEMs) that allow representation of differential equations and previously unrepresentable situations while preserving causality definitions.
Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical systems, runs into several problems. We introduce GSEMs (generalized SEMs), a flexible generalization of SEMs that directly specify the results of interventions, in which (1) systems of differential equations can be represented in a natural and intuitive manner, (2) certain natural situations, which cannot be represented by SEMs at all, can be represented easily, (3) the definition of actual causality in SEMs carries over essentially without change.