Restructuring Dynamic Causal Systems in Equilibrium
In this paper I consider general obstacles to the recovery of a causal system from its probability distribution. I argue that most of the well-known problems with this task belong in the class of what I call degenerate causal systems. I then consider the task of discovering causality of dynamic systems that have passed through one or more equilibrium points, and show that these systems present a challenge to causal discovery that is fundamentally different from degeneracy. To make this comparison, I consider two operators that are used to transform causal models. The first is the well-known Do operator for modeling manipulation, and the second is the Equilibration operator for modeling a dynamic system that has achieved equilibrium. I consider a set of questions regarding the commutability of these operators i.e., whether or not an equilibrated-manipulated model is necessarily equal to the corresponding manipulated-equilibrated model, and I explore the implications of that commutability on the practice of causal discovery. I provide empirical results showing that (a) these two operators sometimes, but not always, commute, and (b) the manipulatedequilibrated model is the correct one under a common interpretation of manipulation on dynamic systems. I argue that these results have strong implications for causal discovery from equilibrium data.