Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks

TL;DR

This paper introduces a method for modeling uncertain evidence in Bayesian networks using credal networks, enabling reliable evidence propagation and efficient computation, especially with multiple uncertain evidences.

Contribution

It proposes a set-valued quantification approach for uncertain evidence in Bayesian networks and reduces evidence propagation to standard updating in augmented credal networks.

Findings

Evidence propagation can be reduced to standard updating in credal networks.

An efficient exact procedure is developed for a subclass of instances.

The method provides a set-valued version of opinion pooling for multiple evidences.

Abstract

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.