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

TL;DR

This paper introduces an efficient message-passing algorithm for credal nets based on epistemic irrelevance, enabling better belief updating in imprecise probabilistic models, especially in tree-structured graphs.

Contribution

It develops a linear-time, exact message-passing algorithm for credal nets using epistemic irrelevance, expanding the theoretical and practical tools for imprecise probability models.

Findings

Algorithm is linear in the number of nodes.

The approach satisfies key rationality requirements.

Application to online character recognition demonstrates practical advantages.

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.