Valuation Networks and Conditional Independence

TL;DR

This paper explores how valuation networks serve as graphical tools to represent various uncertainty models, including probability, belief functions, and possibility theories, and demonstrates their ability to encode conditional independence relations.

Contribution

It introduces how valuation networks encode conditional independence across multiple uncertainty calculi, unifying various probabilistic and belief models within a graphical framework.

Findings

Valuation networks encode conditional independence relations.

They encompass undirected, directed, and causal graph models.

The framework unifies different uncertainty theories.

Abstract

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.