Advertisement

Lifted Maximum Expected Utility

  • Marcel GehrkeEmail author
  • Tanya Braun
  • Ralf Möller
  • Alexander Waschkau
  • Christoph Strumann
  • Jost Steinhäuser
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11326)

Abstract

The lifted junction tree algorithm (LJT) answers multiple queries efficiently for relational models under uncertainties by building and then reusing a first-order cluster representation. We extend the underling model representation of LJT, which is called parameterised probabilistic model, to calculate a lifted solution to the maximum expected utility (MEU) problem. Specifically, this paper contributes (i) action and utility nodes for parameterised probabilistic models, resulting in parameterised probabilistic decision models and (ii) meuLJT, an algorithm to solve the MEU problem using parameterised probabilistic decision models efficiently, while also being able to answer multiple marginal queries.

References

  1. 1.
    Apsel, U., Brafman, R.I.: Extended lifted inference with joint formulas. In: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, pp. 11–18. AUAI Press (2011)Google Scholar
  2. 2.
    Braun, T., Möller, R.: Lifted junction tree algorithm. In: Friedrich, G., Helmert, M., Wotawa, F. (eds.) KI 2016. LNCS (LNAI), vol. 9904, pp. 30–42. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-46073-4_3CrossRefGoogle Scholar
  3. 3.
    Braun, T., Möller, R.: Parameterised queries and lifted query answering. In: IJCAI, pp. 4980–4986 (2018)Google Scholar
  4. 4.
    Gehrke, M., Braun, T., Möller, R.: Lifted dynamic junction tree algorithm. In: Chapman, P., Endres, D., Pernelle, N. (eds.) ICCS 2018. LNCS (LNAI), vol. 10872, pp. 55–69. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-91379-7_5CrossRefGoogle Scholar
  5. 5.
    Joshi, S., Kersting, K., Khardon, R.: Generalized first order decision diagrams for first order Markov decision processes. In: IJCAI, pp. 1916–1921 (2009)Google Scholar
  6. 6.
    Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. J. Roy. Stat. Soc. Ser. B (Methodol.) 50(2), 157–224 (1988)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Milch, B., Zettlemoyer, L.S., Kersting, K., Haimes, M., Kaelbling, L.P.: Lifted probabilistic inference with counting formulas. In: Proceedings of AAAI, vol. 8, pp. 1062–1068 (2008)Google Scholar
  8. 8.
    Nath, A., Domingos, P.: A language for relational decision theory. In: Proceedings of the International Workshop on Statistical Relational Learning (2009)Google Scholar
  9. 9.
    Nath, A., Domingos, P.: Efficient lifting for online probabilistic inference. In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, pp. 1193–1198. AAAI Press (2010)Google Scholar
  10. 10.
    Nath, A., Domingos, P.M.: Efficient belief propagation for utility maximization and repeated inference. In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, pp. 1187–1192. AAAI Press (2010)Google Scholar
  11. 11.
    Poole, D.: First-order probabilistic inference. In: Proceedings of IJCAI, vol. 3, pp. 985–991 (2003)Google Scholar
  12. 12.
    de Salvo Braz, R.: Lifted first-order probabilistic inference. Ph.D. thesis, Ph. D. dissertation, University of Illinois at Urbana Champaign (2007)Google Scholar
  13. 13.
    de Salvo Braz, R., Amir, E., Roth, D.: MPE and partial inversion in lifted probabilistic variable elimination. In: AAAI, vol. 6, pp. 1123–1130 (2006)Google Scholar
  14. 14.
    Sanner, S., Boutilier, C.: Approximate solution techniques for factored first-order MDPs. In: 17th International Conference on Automated Planning and Scheduling, ICAPS 2007, pp. 288–295. AAAI Press (2007)Google Scholar
  15. 15.
    Sanner, S., Kersting, K.: Symbolic dynamic programming for first-order POMDPs. In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, pp. 1140–1146. AAAI Press (2010)Google Scholar
  16. 16.
    Steinhäuser, J., Kühlein, T.: Role of the general practitioner. In: Gombotz, H., Zacharowski, K., Spahn, D.R. (eds.) Patient Blood Management, pp. 61–65. Thieme, Stuttgart (2015)Google Scholar
  17. 17.
    Taghipour, N., Fierens, D., Davis, J., Blockeel, H.: Lifted variable elimination: decoupling the operators from the constraint language. J. Artif. Intell. Res. 47(1), 393–439 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Theodorsson, E.: Uncertainty in measurement and total error: tools for coping with diagnostic uncertainty. Clin. Lab. Med. 37(1), 15–34 (2017)CrossRefGoogle Scholar
  19. 19.
    Wemmenhove, B., Mooij, J.M., Wiegerinck, W., Leisink, M., Kappen, H.J., Neijt, J.P.: Inference in the promedas medical expert system. In: Bellazzi, R., Abu-Hanna, A., Hunter, J. (eds.) AIME 2007. LNCS (LNAI), vol. 4594, pp. 456–460. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-73599-1_61CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Information SystemsUniversity of LübeckLübeckGermany
  2. 2.Institute of Family MedicineUniversity Medical Center Schleswig-HolsteinLübeckGermany

Personalised recommendations