Charles University, Faculty of Mathematicsand Physics
Prague, Czech Republic
16-19 July 2007


Andrés Cano, Manuel Gómez, Serafí­n Moral

Credal Nets with Probabilities Estimated with an Extreme Imprecise Dirichlet Model


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

Paper Download

The paper is availabe in the following formats:

Authors addresses:

Andrés Cano
Dpto. Ciencias de la Computación e I.A.
ETS Ingeniería Informática
Avda. Andalucia s/n
Granada 18071

Manuel Gómez
Dpto. Ciencias de la Computación e I.A.
E.T.S. Ingeniería Informática
C// Periodista Daniel Saucedo Aranda
18071 Granada

Serafí­n Moral
Dpto. Ciencias de la Computación e IA
ETSI Informática
Universidad de Granada
18071 Granada

E-mail addresses:

Andrés Cano
Manuel Gómez
Serafí­n Moral

[ back to the Proceedings of ISIPTA'07 home page 
Send any remarks to the following address: