Structural Controllability and Observability in Influence Diagrams

TL;DR

This paper explores the structural controllability and observability of influence diagrams, providing theorems and algorithms to analyze the structural properties of probabilistic models without requiring specific numerical data.

Contribution

It introduces new structural controllability and observability theorems for influence diagrams, along with algorithms to analyze these properties based solely on model structure.

Findings

Developed structural controllability theorems for influence diagrams.

Formulated algorithms for structural observability analysis.

Enhanced understanding of probabilistic model structure and dependencies.

Abstract

Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are fundamental concepts in dynamic systems (Luenberger 1979). Controllability corresponds to the ability to control a system while observability analyzes the inferability of its variables. Both properties can be determined by the ranks of the system matrices. Structural controllability and observability, on the other hand, analyze the property of a system with its structure only, without the specific knowledge of the values of its elements (tin 1974, Shields and Pearson 1976). The structural analysis explores the connection between the structure of a model and the functional dependence among its elements. It is useful in comprehending problem and formulating solution by challenging the underlying intuitions and detecting inconsistency in a model. This type of qualitative reasoning can sometimes provide insight even when there is insufficient numerical information in a model.