From Deterministic ODEs to Dynamic Structural Causal Models

Abstract

Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship between Ordinary Differential Equations and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be modelled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria.

arXiv commentAccepted for publication in Conference on Uncertainy in Artificial Intelligence

References in corpus (4)

• Directed Cyclic Graphical Representations of Feedback Models
• From Ordinary Differential Equations to Structural Causal Models: the deterministic case
• Causal interpretation of stochastic differential equations
• Learning Why Things Change: The Difference-Based Causality Learner

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• Causal Navigation by Continuous-time Neural Networks
• Beyond Structural Causal Models: Causal Constraints Models
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• Dynamic Causal Bayesian Optimization
• Identifying Causal Structure in Dynamical Systems