5th International Symposium on Imprecise Probability: Theories and Applications Prague Czech Republic

5th International Symposium on Imprecise Probability: Theories and Applications, Prague, Czech Republic, 2007 Credal Nets with Probabilities Estimated with an Extreme Imprecise Dirichlet Model A. Cano, M. Gomez-Olmedo, S. Moral Dpto. Ciencias de la Computacion Universidad de Granada 18071 - Granada (Spain) (acu,mgomez,smc)@decsai.ugr.es Abstract The propagation of probabilities in credal networks when probabilities are estimated with a global impre- cise Dirichlet model is an important open problem. Only Zaffalon [21] has proposed an algorithm for the Naive classifier. The main difficulty is that, in gen- eral, computing upper and lower probability intervals implies the resolution of an optimization of a fraction of two polynomials. In the case of the Naive credal classifier, Zaffalon has shown that the function is a convex function of only one parameter, but there is not a similar result for general credal sets. In this pa- per, we propose the use of an imprecise global model, but we restrict the distributions to only the most ex- treme ones. The result is a model giving rise that in the case of estimating a conditional probability under independence relationships, it can produce smaller in- tervals than the global general model. Its main ad- vantage is that the optimization problem is simpler, and available procedures can be directly applied, as the ones proposed in [7].

• variable dx


• conditional probabilities


• decision variable


• when considering


• global application


• treme ones


• conditional probability


• credal networks