Approximate Separability for Weak Interaction in Dynamic Systems

One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact propagation of marginals for prediction. This paper addresses two questions left open by the earlier paper: can we define a notion of approximate separability that occurs naturally in practice, and do separability and approximate separability lead to accurate monitoring? The answer to both questions is affirmative. The paper also analyzes the structure of approximately separable decompositions, and provides some explanation as to why these models perform well.