Causal Modeling With Infinitely Many Variables

TL;DR

This paper introduces GSEMs, a flexible extension of SEMs that can naturally model systems with infinitely many variables, including differential equations and cases impossible for traditional SEMs, while preserving causality concepts.

Contribution

The paper proposes GSEMs, a generalized framework for causal modeling with infinitely many variables, addressing limitations of traditional SEMs in dynamical and complex systems.

Findings

GSEMs can represent differential equations naturally.

Certain complex systems are representable by GSEMs but not SEMs.

Causality definitions extend to GSEMs without major changes.

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.