Irrelevance and Independence Relations in Quasi-Bayesian Networks

Abstract

This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can irrelevance/independence relations in Quasi-Bayesian networks be detected, enforced and exploited? This paper addresses these questions through Walley's definitions of irrelevance and independence. Novel algorithms and results are presented for inferences with the so-called natural extensions using fractional linear programming, and the properties of the so-called type-1 extensions are clarified through a new generalization of d-separation.

Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998)

References in corpus (5)

• Independence Concepts for Convex Sets of Probabilities
• Robustness Analysis of Bayesian Networks with Local Convex Sets of Distributions
• Decision Making with Interval Influence Diagrams
• Independence with Lower and Upper Probabilities
• Propagation of 2-Monotone Lower Probabilities on an Undirected Graph

Cited by in corpus (2)

• Separation Properties of Sets of Probability Measures
• Credal Networks under Maximum Entropy