Solving Hybrid Influence Diagrams with Deterministic Variables

Yijing Li, Prakash Shenoy
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:309-318, 2010.

Abstract

We describe a framework and an algo- rithm for solving hybrid influence diagrams with discrete, continuous, and deterministic chance variables, and discrete and continu- ous decision variables. A continuous chance variable in an influence diagram is said to be deterministic if its conditional distributions have zero variances. The solution algorithm is an extension of Shenoy’s fusion algorithm for discrete influence diagrams. We describe an extended Shenoy-Shafer architecture for propagation of discrete, continuous, and util- ity potentials in hybrid influence diagrams that include deterministic chance variables. The algorithm and framework are illustrated by solving two small examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-li10a, title = {Solving Hybrid Influence Diagrams with Deterministic Variables}, author = {Li, Yijing and Shenoy, Prakash}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {309--318}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/li10a/li10a.pdf}, url = {https://proceedings.mlr.press/r8/li10a.html}, abstract = {We describe a framework and an algo- rithm for solving hybrid influence diagrams with discrete, continuous, and deterministic chance variables, and discrete and continu- ous decision variables. A continuous chance variable in an influence diagram is said to be deterministic if its conditional distributions have zero variances. The solution algorithm is an extension of Shenoy’s fusion algorithm for discrete influence diagrams. We describe an extended Shenoy-Shafer architecture for propagation of discrete, continuous, and util- ity potentials in hybrid influence diagrams that include deterministic chance variables. The algorithm and framework are illustrated by solving two small examples.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Solving Hybrid Influence Diagrams with Deterministic Variables %A Yijing Li %A Prakash Shenoy %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-li10a %I PMLR %P 309--318 %U https://proceedings.mlr.press/r8/li10a.html %V R8 %X We describe a framework and an algo- rithm for solving hybrid influence diagrams with discrete, continuous, and deterministic chance variables, and discrete and continu- ous decision variables. A continuous chance variable in an influence diagram is said to be deterministic if its conditional distributions have zero variances. The solution algorithm is an extension of Shenoy’s fusion algorithm for discrete influence diagrams. We describe an extended Shenoy-Shafer architecture for propagation of discrete, continuous, and util- ity potentials in hybrid influence diagrams that include deterministic chance variables. The algorithm and framework are illustrated by solving two small examples. %Z Reissued by PMLR on 04 October 2026.
APA
Li, Y. & Shenoy, P.. (2010). Solving Hybrid Influence Diagrams with Deterministic Variables. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:309-318 Available from https://proceedings.mlr.press/r8/li10a.html. Reissued by PMLR on 04 October 2026.

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