Structural Controllability and Observability in Influence Diagrams
This work addresses the challenge of qualitative reasoning in probabilistic models for researchers in dynamic systems and AI, but it appears incremental as it extends existing structural analysis concepts to influence diagrams.
The paper tackles the problem of analyzing controllability and observability in influence diagrams by developing structural theorems and algorithms, focusing on the connection between model structure and functional dependencies without requiring specific numerical values.
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.