Conditional Independence in Uncertainty Theories

TL;DR

This paper generalizes the concepts of independence and conditional independence within valuation-based systems, unifying their definitions across various uncertainty theories like probability, belief functions, and possibility theory.

Contribution

It introduces a unified axiomatic framework for independence in VBS that encompasses multiple uncertainty calculi, extending classical probability concepts.

Findings

Definitions generalize probability independence to other theories

Applicable to Dempster-Shafer belief functions

Works within a broad axiomatic framework

Abstract

This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and conditional independence in terms of factorization of the joint valuation. The definitions of independence and conditional independence in VBS generalize the corresponding definitions in probability theory. Our definitions apply not only to probability theory, but also to Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory. In fact, they apply to any uncertainty calculi that fit in the framework of valuation-based systems.