Abstract
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.
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Notes
- 1.
Sensitivity analysis does not require the specification of more general class of models, being only focused on the results of the inferences. Thus, it should be regarded as a different topic, which, as a matter of fact, received more attention (e.g., [14]).
- 2.
The solution of a linear program is an extreme point of the feasible region.
References
Hugin Expert network repository. http://www.hugin.com/technology/samples
Benferhat, S., Smaoui, S.: Hybrid possibilistic networks. Int. J. Approximate Reasoning 44(3), 224–243 (2007)
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)
Cozman, F.G.: Credal networks. Artif. Intell. 120, 199–233 (2000)
de Campos, L.M., Huete, J.F., Moral, S.: Probability intervals: a tool for uncertain reasoning. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 2(02), 167–196 (1994)
Fagiuoli, E., Zaffalon, M.: Decisions under uncertainty with credal influence diagrams. Technical report, pp. 51–98, IDSIA (1998). (unpublished)
Fertig, K.W., Breese, J.S.: Probability intervals over influence diagrams. IEEE Trans. Pattern Anal. Mach. Intell. 15(3), 280–286 (1993)
Howard, R.A., Matheson, J.E.: Influence diagram retrospective. Decision Anal. 2(3), 144–147 (2005)
Huntley, N., Troffaes, M.C.M.: Normal form backward induction for decision trees with coherent lower previsions. Ann. Oper. Res. 195(1), 111–134 (2012)
Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs. Springer Verlag, New York (2007)
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)
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)
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)
Nielsen, T.D., Jensen, F.V.: Sensitivity analysis in influence diagrams. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 33(2), 223–234 (2003)
Raiffa, H.: Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Addison-Wesley, Boston (1968)
Shenoy, P.P.: Valuation-based systems for Bayesian decision analysis. Oper. Res. 40(3), 463–484 (1992)
Xu, H., Smets, P.: Reasoning in evidential networks with conditional belief functions. Int. J. Approximate Reasoning 14(2–3), 155–185 (1996)
Zhang, N.L., Poole, D.: Exploiting causal independence in Bayesian network inference. J. Artif. Intell. Res. 5, 301–328 (1996)
Acknowledgments
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.
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Cabañas, R., Antonucci, A., Cano, A., Gómez-Olmedo, M. (2015). Variable Elimination for Interval-Valued Influence Diagrams. In: Destercke, S., Denoeux, T. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2015. Lecture Notes in Computer Science(), vol 9161. Springer, Cham. https://doi.org/10.1007/978-3-319-20807-7_49
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