DeepAI AI Chat
Log In Sign Up

Conditional Independence in Uncertainty Theories

03/13/2013
by   Prakash P. Shenoy, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

page 5

page 6

page 7

page 8

03/06/2013

Valuation Networks and Conditional Independence

Valuation networks have been proposed as graphical representations of va...
12/14/2018

Factorization of Dempster-Shafer Belief Functions Based on Data

One important obstacle in applying Dempster-Shafer Theory (DST) is its r...
02/27/2013

An Ordinal View of Independence with Application to Plausible Reasoning

An ordinal view of independence is studied in the framework of possibili...
09/15/2017

A Semantic Approach to the Analysis of Rewriting-Based Systems

Properties expressed as the provability of a first-order sentence can be...
07/13/2017

On (Anti)Conditional Independence in Dempster-Shafer Theory

This paper verifies a result of Shenoy:94 concerning graphoidal structur...
02/14/2023

A Complication for the Many Worlds Theory

The Many Worlds Theory and the Independence Postulate are in conflict, a...
10/12/2021

The Sigma-Max System Induced from Randomness and Fuzziness

This paper managed to induce probability theory (sigma system) and possi...