Valuation Networks and Conditional Independence
This work provides a theoretical foundation for unifying graphical representations in uncertainty reasoning, which is incremental as it extends existing valuation network frameworks.
The paper tackles the problem of understanding how valuation networks encode conditional independence relations across multiple uncertainty calculi, and shows that in the probabilistic case, these networks encompass various graphical models like undirected and directed acyclic graphs.
Valuation networks have been proposed as graphical representations of valuation-based systems (VBSs). The VBS framework is able to capture many uncertainty calculi including probability theory, Dempster-Shafer's belief-function theory, Spohn's epistemic belief theory, and Zadeh's possibility theory. In this paper, we show how valuation networks encode conditional independence relations. For the probabilistic case, the class of probability models encoded by valuation networks includes undirected graph models, directed acyclic graph models, directed balloon graph models, and recursive causal graph models.