Beyond Structural Causal Models: Causal Constraints Models
This work addresses a foundational problem in causal modeling for researchers in AI and statistics, offering a more flexible framework for representing equilibrium systems.
The paper tackles the limitation of Structural Causal Models (SCMs) in representing dynamical systems at equilibrium by proposing Causal Constraints Models (CCMs), proving that CCMs capture the causal semantics of such systems and illustrating this with examples from differential equations and chemical reactions.
Structural Causal Models (SCMs) provide a popular causal modeling framework. In this work, we show that SCMs are not flexible enough to give a complete causal representation of dynamical systems at equilibrium. Instead, we propose a generalization of the notion of an SCM, that we call Causal Constraints Model (CCM), and prove that CCMs do capture the causal semantics of such systems. We show how CCMs can be constructed from differential equations and initial conditions and we illustrate our ideas further on a simple but ubiquitous (bio)chemical reaction. Our framework also allows to model functional laws, such as the ideal gas law, in a sensible and intuitive way.