###
ISIPTA'07 -
FIFTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

###
Charles University, Faculty of Mathematicsand Physics

Prague, Czech Republic

16-19 July 2007

## ELECTRONIC PROCEEDINGS

## Andrés Cano, Manuel Gómez, Serafín Moral

# Credal Nets with Probabilities Estimated with an Extreme Imprecise Dirichlet Model

### Abstract

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

Spain

Manuel Gómez

Dpto. Ciencias de la ComputaciÃ³n e I.A.

E.T.S. IngenierÃa InformÃ¡tica

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: **

[ back
to the Proceedings of ISIPTA'07 home page ]

Send any remarks to the following address:
smc@decsai.ugr.es