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A Framework for Solving Hybrid Influence Diagrams Containing Deterministic Conditional Distributions

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  • Yijing Li

    (University of Kansas School of Business, Lawrence, Kansas 66045)

  • Prakash P. Shenoy

    (University of Kansas School of Business, Lawrence, Kansas 66045)

Abstract

We describe a framework and an algorithm for approximately solving a class of hybrid influence diagrams (IDs) containing discrete and continuous chance variables, discrete and continuous decision variables, and deterministic conditional distributions for chance variables. A conditional distribution for a chance variable is said to be deterministic if its variances, for each state of its parents, are all zeroes. The solution algorithm is an extension of Shenoy's fusion algorithm for discrete influence diagrams. To mitigate the integration and optimization problems associated with solving hybrid IDs, we propose using mixture of polynomials approximations of conditional probability density and utility functions and piecewise linear approximations of nonlinear deterministic conditional distributions for continuous chance variables. The class of hybrid IDs that can be solved by our framework are those that do not involve divisions. The framework and algorithm are illustrated by solving two small examples of hybrid IDs.

Suggested Citation

  • Yijing Li & Prakash P. Shenoy, 2012. "A Framework for Solving Hybrid Influence Diagrams Containing Deterministic Conditional Distributions," Decision Analysis, INFORMS, vol. 9(1), pages 55-75, March.
    • Handle: RePEc:inm:ordeca:v:9:y:2012:i:1:p:55-75
    DOI: 10.1287/deca.1120.0230
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    References listed on IDEAS

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    4. Salo, Ahti & Andelmin, Juho & Oliveira, Fabricio, 2022. "Decision programming for mixed-integer multi-stage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 299(2), pages 550-565.

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