Causal Modeling With Infinitely Many Variables

Abstract

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.