Approximate Separability for Weak Interaction in Dynamic Systems

TL;DR

This paper introduces the concept of approximate separability in dynamic systems, demonstrating its practical relevance and effectiveness for monitoring weakly interacting subsystems, and analyzing why such models perform well.

Contribution

It defines a notion of approximate separability, shows its practical occurrence, and explains the structure and effectiveness of these decompositions in dynamic system monitoring.

Findings

Approximate separability occurs naturally in practice.

Models based on approximate separability perform well in monitoring.

The paper provides structural analysis of approximately separable decompositions.

Abstract

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 afirmative. The paper also analyzes the structure of approximately separable decompositions, and provides some explanation as to why these models perform well.