Epistemic irrelevance in credal nets: The case of imprecise Markov trees

https://doi.org/10.1016/j.ijar.2010.08.011Get rights and content
Under an Elsevier user license
open archive

Abstract

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm’s operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.

Keywords

Coherence
Credal net
Epistemic irrelevance
Strong independence
Separation
Hidden Markov model

Cited by (0)