Multi-currency Influence Diagrams

Søren Holbech Nielsen, Thomas Dyhre Nielsen, Finn V. Jensen

Research output: Contribution to book/anthology/report/conference proceedingBook chapterResearch

3 Citations (Scopus)
224 Downloads (Pure)

Abstract

When using the influence diagrams framework for solving a decision problem with several different quantitative utilities, the traditional approach has been to convert the utilities into one common currency. This conversion is carried out using a tacit transformation, under the assumption that the converted problem is equivalent to the original one. In this paper we present an extension of the influence diagram framework. The extension allows for these decision problems to be modelled in their original form. We present an algorithm that, given a linear conversion function between the currencies of the original utilities, discovers a characterisation of all other such functions, which induce the same optimal strategy. As this characterisation can potentially be very complex, we give methods to present it in an approximate way.
Original languageEnglish
Title of host publicationAdvances in Probabilistic Graphical Models
EditorsPeter Lucas, José Gamez, Antonio Salmeron
Volume213
PublisherSpringer
Publication date2007
Pages275-294
ISBN (Print)978-3-540-68994-2, 354068994X
Publication statusPublished - 2007
SeriesStudies in Fuzziness and Soft Computing
Volume213
ISSN1434-9922

Keywords

  • Decision Processes
  • Inference
  • Learning
  • Probabilistic Graphical Models

Cite this

Nielsen, S. H., Nielsen, T. D., & Jensen, F. V. (2007). Multi-currency Influence Diagrams. In P. Lucas, J. Gamez, & A. Salmeron (Eds.), Advances in Probabilistic Graphical Models (Vol. 213, pp. 275-294). Springer. Studies in Fuzziness and Soft Computing, Vol.. 213
Nielsen, Søren Holbech ; Nielsen, Thomas Dyhre ; Jensen, Finn V. / Multi-currency Influence Diagrams. Advances in Probabilistic Graphical Models. editor / Peter Lucas ; José Gamez ; Antonio Salmeron. Vol. 213 Springer, 2007. pp. 275-294 (Studies in Fuzziness and Soft Computing, Vol. 213).
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Nielsen, SH, Nielsen, TD & Jensen, FV 2007, Multi-currency Influence Diagrams. in P Lucas, J Gamez & A Salmeron (eds), Advances in Probabilistic Graphical Models. vol. 213, Springer, Studies in Fuzziness and Soft Computing, vol. 213, pp. 275-294.

Multi-currency Influence Diagrams. / Nielsen, Søren Holbech; Nielsen, Thomas Dyhre; Jensen, Finn V.

Advances in Probabilistic Graphical Models. ed. / Peter Lucas; José Gamez; Antonio Salmeron. Vol. 213 Springer, 2007. p. 275-294.

Research output: Contribution to book/anthology/report/conference proceedingBook chapterResearch

TY - CHAP

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AB - When using the influence diagrams framework for solving a decision problem with several different quantitative utilities, the traditional approach has been to convert the utilities into one common currency. This conversion is carried out using a tacit transformation, under the assumption that the converted problem is equivalent to the original one. In this paper we present an extension of the influence diagram framework. The extension allows for these decision problems to be modelled in their original form. We present an algorithm that, given a linear conversion function between the currencies of the original utilities, discovers a characterisation of all other such functions, which induce the same optimal strategy. As this characterisation can potentially be very complex, we give methods to present it in an approximate way.

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Nielsen SH, Nielsen TD, Jensen FV. Multi-currency Influence Diagrams. In Lucas P, Gamez J, Salmeron A, editors, Advances in Probabilistic Graphical Models. Vol. 213. Springer. 2007. p. 275-294. (Studies in Fuzziness and Soft Computing, Vol. 213).