We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine the local credal sets in the networks into an overall joint model, and use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the network. The algorithm, which is essentially linear in the number of nodes, is formulated entirely in terms of coherent lower previsions. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of the model for prediction.
Keywords. Coherence, credal network, epistemic irrelevance, epistemic independence, strong independence, imprecise Markov tree, separation, hidden Markov chain.
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Authors addresses:
Gert De Cooman
Technologiepark - Zwijnaarde 914
9052 Zwijnaarde
Filip Hermans
Technologiepark-Zwijnaarde 914
9052 Zwijnaarde
Alessandro Antonucci
c/o IDSIA
Galleria 2
CH-6928 Manno (Lugano)
Marco Zaffalon
Galleria 2
CH-6928 Manno
Switzerland
E-mail addresses:
| Gert De Cooman | gert.decooman@ugent.be |
| Filip Hermans | filip.hermans@ugent.be |
| Alessandro Antonucci | alessandro@idsia.ch |
| Marco Zaffalon | zaffalon@idsia.ch |