Advertisement

European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty

ECSQARU 2015: Symbolic and Quantitative Approaches to Reasoning with Uncertainty pp 541-551 | Cite as

Variable Elimination for Interval-Valued Influence Diagrams

  • Rafael Cabañas
  • Alessandro Antonucci
  • Andrés Cano
  • Manuel Gómez-Olmedo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9161)

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.

Keywords

Influence diagrams Bayesian networks Credal networks Sequential decision making Imprecise probability 

Notes

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.

References

  1. 1.
    Hugin Expert network repository. http://www.hugin.com/technology/samples
  2. 2.
    Benferhat, S., Smaoui, S.: Hybrid possibilistic networks. Int. J. Approximate Reasoning 44(3), 224–243 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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
  4. 4.
    Cozman, F.G.: Credal networks. Artif. Intell. 120, 199–233 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fagiuoli, E., Zaffalon, M.: Decisions under uncertainty with credal influence diagrams. Technical report, pp. 51–98, IDSIA (1998). (unpublished)Google Scholar
  7. 7.
    Fertig, K.W., Breese, J.S.: Probability intervals over influence diagrams. IEEE Trans. Pattern Anal. Mach. Intell. 15(3), 280–286 (1993)CrossRefGoogle Scholar
  8. 8.
    Howard, R.A., Matheson, J.E.: Influence diagram retrospective. Decision Anal. 2(3), 144–147 (2005)CrossRefGoogle Scholar
  9. 9.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs. Springer Verlag, New York (2007)CrossRefzbMATHGoogle Scholar
  11. 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. 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. 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
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    Raiffa, H.: Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Addison-Wesley, Boston (1968)zbMATHGoogle Scholar
  16. 16.
    Shenoy, P.P.: Valuation-based systems for Bayesian decision analysis. Oper. Res. 40(3), 463–484 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Xu, H., Smets, P.: Reasoning in evidential networks with conditional belief functions. Int. J. Approximate Reasoning 14(2–3), 155–185 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Zhang, N.L., Poole, D.: Exploiting causal independence in Bayesian network inference. J. Artif. Intell. Res. 5, 301–328 (1996)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Rafael Cabañas
    • 1
  • Alessandro Antonucci
    • 2
  • Andrés Cano
    • 1
  • Manuel Gómez-Olmedo
    • 1
  1. 1.Department of Computer Science and Artificial Intelligence CITICUniversity of GranadaGranadaSpain
  2. 2.Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA)Manno-LuganoSwitzerland

Personalised recommendations