The propagation of probabilities in credal networks when probabilities are estimated with a global imprecise Dirichlet model is an important open problem. Only Zaffalon (2001) has proposed an algorithm for the Naive classifier. The main difficulty is that, in general, computing upper and lower probability intervals implies the resolution of an optimization of a fraction of two polynomials. In the case of the Naive Bayes, Zaffalon has shown that the function is a convex function of one parameter, but this is not true at the general case. In this paper, we propose the use of an imprecise global model, but we restrict the distributions to only two (the most extreme ones). The result is a model giving rise to the same upper and lower probabilities, when estimating the uncertainty of a future event, but in the case of estimating a conditional probability, will provide smaller intervals. Its main advantage is that the optimization problem is simpler, and available procedures can be directly applied, as the ones proposed in Cano et al. (2007).
Keywords. Locally specified redal networks, global imprecise Dirichlet model, propagation algorithms, probability trees
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Authors addresses:
Andrés Cano
Dpto. Ciencias de la Computación e I.A.
ETS Ingeniería Informática
Avda. Andalucia s/n
Granada 18071
Spain
Manuel Gómez
Dpto. Ciencias de la Computación e I.A.
E.T.S. IngenierÃa Informática
C// Periodista Daniel Saucedo Aranda
18071 Granada
Serafín Moral
Dpto. Ciencias de la Computación e IA
ETSI Informática
Universidad de Granada
18071 Granada
SPAIN
E-mail addresses:
| Andrés Cano | acu@decsai.ugr.es |
| Manuel Gómez | mgomez@decsai.ugr.es |
| Serafín Moral | smc@decsai.ugr.es |