Variable Elimination for Interval-Valued Influence Diagrams
Influence diagrams are probabilistic graphical models used to represent and solve decision problems under uncertainty. Sharp numerical values are required to quantify probabilities and utilities. Yet, real models are based on data streams provided by partially reliable sensors or experts. We propose an interval-valued quantification of these parameters to gain realism in the modelling and to analyse the sensitivity of the inferences with respect to perturbations of the sharp values. An extension of the classical influence diagrams formalism to support interval-valued potentials is provided. Moreover, a variable elimination algorithm especially designed for these models is developed and evaluated in terms of complexity and empirical performances.
KeywordsInfluence diagrams Bayesian networks Credal networks Sequential decision making Imprecise probability
This research was supported by the Spanish Ministry of Economy and Competitiveness under project TIN2013-46638-C3-2-P, the European Regional Development Fund (FEDER), the FPI scholarship program (BES-2011-050604) and the short stay in foreign institutions scholarship EEBB-I-14-08102. The authors have also been partially supported by “Junta de Andalucía” under projects TIC-06016 and P08-TIC-03717.
- 1.Hugin Expert network repository. http://www.hugin.com/technology/samples
- 3.Bielza, C., Gómez, M., Insua, S.R., del Pozo, J.A.F., Barreno, P.G., Caballero, S., Luna, M.S.: IctNEO system for jaundice management. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 92(4), 307–315 (1998)Google Scholar
- 6.Fagiuoli, E., Zaffalon, M.: Decisions under uncertainty with credal influence diagrams. Technical report, pp. 51–98, IDSIA (1998). (unpublished)Google Scholar
- 11.Kikuti, D., Cozman, F.G., de Campos, C.P.: Partially ordered preferences in decision trees: computing strategies with imprecision in probabilities. In: IJCAI Workshop on Advances in Preference Handling, pp. 118–123 (2005)Google Scholar
- 12.Kjaerulff, U.: Triangulation of graphs - algorithms giving small total state space. Research report R-90-09, Department of Mathematics and Computer Science, Aalborg University, Denmark (1990)Google Scholar
- 13.Lucas, P.J.F., Taal, B.: Computer-based decision support in the management of primary gastric non-hodgkin lymphoma. In: UU-CS, vol. 33 (1998)Google Scholar