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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Dpto. Ciencias de la Computación e I.A.
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Dpto. Ciencias de la ComputaciÃ³n e I.A.
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C// Periodista Daniel Saucedo Aranda
Dpto. Ciencias de la Computación e IA
Universidad de Granada