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Applying Numerical Trees to Evaluate Asymmetric Decision Problems

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2711))

Abstract

This paper describes some ideas for applying numerical trees in order to represent and solve asymmetric decision problems with influence diagrams (IDs). Constraint rules are used to represent the asymmetries between the variables of the ID. These rules will be transformed into numerical trees during the evaluation of the ID. The application of numerical trees can reduce the number of operations required to evaluate the ID. The paper also presents how numerical trees may be approximated, thereby enabling complex decision problems to be evaluated.

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References

  1. Bielza, C., Shenoy, P.P.: A comparison of graphical techniques for asymmetric decision problems. Management Science 45(11), 1552–1569 (1999)

    Article  MATH  Google Scholar 

  2. Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D.: Context-specific independence in Bayesian networks. In: Proceedings of the Twelfth Annual Conference on Uncertainty in Artificial Intelligence (UAI 1996), Portland, Oregon, pp. 115–123 (1996)

    Google Scholar 

  3. Cano, A., Moral, S.: Propagación exacta y aproximada mediante árboles de probabilidad en redes causales. In: Actas de la VII Conferencia de la Asociación Española para la Inteligencia Artificial, Málaga, pp. 635–644 (1997)

    Google Scholar 

  4. Cano, A., Moral, S., Salmerón, A.: Penniless propagation in join trees. International Journal of Intelligent Systems 15(11), 1027–1059 (2000)

    Article  MATH  Google Scholar 

  5. Cano, A., Moral, S., Salmerón, A.: Lazy evaluation in penniless propagation over join trees. Networks 39(4), 175–185 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Charnes, J.M., Shenoy, P.P.: A forward monte carlo method for solving influence diagrams using local computation. Technical report, School of Business. University of Kansas. Summerfield Hall. Lawrence, KS 66045-2003 (July 2000)

    Google Scholar 

  7. Covaliu, Z., Oliver, R.M.: Representation and solution of decision problems using sequential decision diagrams. Management science 41(12), 1860–1881 (1995)

    Article  MATH  Google Scholar 

  8. Demirer, R., Shenoy, P.P.: Sequential valuation networks: A new graphical technique for asymmetric decision problems. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 252–265. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Fung, R.M., Shachter, R.D.: Contingent influence diagrams. Technical report, Department of Engineering-Economic Systems, Stanford Univerity, Stanford, Calif. (1990)

    Google Scholar 

  10. Jensen, F.V.: Bayesian Networks and Decision Graphs. Statistics for Engineering and Information Science. Springer, New York (2001)

    Google Scholar 

  11. Kullback, S., Leibler, R.A.: On information and sufficiency. Annals of Mathematical Statistics 22, 76–86 (1951)

    Article  MathSciNet  Google Scholar 

  12. Lauritzen, S.L., Nilsson, D.: Representing and solving decision problems with limited information. Management Science 47(9), 1235–1251 (2001)

    Article  Google Scholar 

  13. Miller, H.J., Miller, W.A.: A comparison of approaches and implementations for automating decision analysis. Reliability Engineering and System Safety, 115–162 (1990)

    Google Scholar 

  14. Nielsen, T.D., Jensen, F.V.: Representing and solving asymmetric bayesian decision problems. In: Boutilier, C., Goldszmidt, M. (eds.) Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI), pp. 416–425 (2000)

    Google Scholar 

  15. Olmsted, S.M.: On representing and solving decision problems. PhD thesis, Department of Engineering-Economic Systems, Stanford University, Stanford, CA (1983)

    Google Scholar 

  16. Qi, R., Zhang, N.L., Poole, D.: Solving asymmetric decision problems with influence diagrams. In: Proc. of the 10th conference on AI, pp. 491–497 (1994)

    Google Scholar 

  17. Salmerón, A., Cano, A., Moral, S.: Importance sampling in Bayesian networks using probability trees. Computational Statistics and Data Analysis 34, 387–413 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. Shachter, R.D.: Evaluating influence diagrams. Operations Research 34, 871–882 (1986)

    Article  MathSciNet  Google Scholar 

  19. Shenoy, P.: Valuation network representation and solution of asymmetric decision problems. European Journal of Operational Research 121(3), 579–608 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  20. Smith, J.E., Holtzman, S., Matheson, J.E.: Structuring conditional relationships in influence diagrams. Operations Research 41(2), 280–297 (1993)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dpt. Computer Science and Artificial Intelligence, E.T.S. Ingeniería Informática, University of Granada, C/ Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Manuel Gómez & Andrés Cano

Authors
  1. Manuel Gómez
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  2. Andrés Cano
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Aalborg University, Fredrik Bajersvej 7E, 9220, Aalborg, Denmark

    Thomas Dyhre Nielsen

  2. Department of Computer Science, Hong Kong University of Science and Technology, ClearWater Bay Road, Kowloon, Hong Kong, China,

    Nevin Lianwen Zhang

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© 2003 Springer-Verlag Berlin Heidelberg

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Gómez, M., Cano, A. (2003). Applying Numerical Trees to Evaluate Asymmetric Decision Problems. In: Nielsen, T.D., Zhang, N.L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2003. Lecture Notes in Computer Science(), vol 2711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45062-7_16

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  • DOI: https://doi.org/10.1007/978-3-540-45062-7_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40494-1

  • Online ISBN: 978-3-540-45062-7

  • eBook Packages: Springer Book Archive

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