On the relationship between graphical and compositional models for the Dempster-Shafer theory of belief functions

Radim Jiroušek, Václav Kratochvı́l, Prakash P. Shenoy
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:259-269, 2023.

Abstract

This paper studies the relationship between graphical and compositional models representing joint belief functions. In probability theory, the class of Bayesian networks (directed graphical models) is equivalent to compositional models. Such an equivalence does not hold for the Dempster-Shafer belief function theory. We show that each directed graphical belief function model can be represented as a compositional model, but the converse does not hold. As there are two composition operators for belief functions, there are two types of compositional models. In studying their relation to graphical models, they are closely connected. Namely, one is more specific than the other. A precise relationship between these two composition operators is described.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-jirousek23a, title = {On the relationship between graphical and compositional models for the {D}empster-{S}hafer theory of belief functions}, author = {Jirou\v{s}ek, Radim and Kratochv{\'\i}l, V\'aclav and Shenoy, Prakash P.}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {259--269}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/jirousek23a/jirousek23a.pdf}, url = {https://proceedings.mlr.press/v215/jirousek23a.html}, abstract = {This paper studies the relationship between graphical and compositional models representing joint belief functions. In probability theory, the class of Bayesian networks (directed graphical models) is equivalent to compositional models. Such an equivalence does not hold for the Dempster-Shafer belief function theory. We show that each directed graphical belief function model can be represented as a compositional model, but the converse does not hold. As there are two composition operators for belief functions, there are two types of compositional models. In studying their relation to graphical models, they are closely connected. Namely, one is more specific than the other. A precise relationship between these two composition operators is described.} }
Endnote
%0 Conference Paper %T On the relationship between graphical and compositional models for the Dempster-Shafer theory of belief functions %A Radim Jiroušek %A Václav Kratochvı́l %A Prakash P. Shenoy %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-jirousek23a %I PMLR %P 259--269 %U https://proceedings.mlr.press/v215/jirousek23a.html %V 215 %X This paper studies the relationship between graphical and compositional models representing joint belief functions. In probability theory, the class of Bayesian networks (directed graphical models) is equivalent to compositional models. Such an equivalence does not hold for the Dempster-Shafer belief function theory. We show that each directed graphical belief function model can be represented as a compositional model, but the converse does not hold. As there are two composition operators for belief functions, there are two types of compositional models. In studying their relation to graphical models, they are closely connected. Namely, one is more specific than the other. A precise relationship between these two composition operators is described.
APA
Jiroušek, R., Kratochvı́l, V. & Shenoy, P.P.. (2023). On the relationship between graphical and compositional models for the Dempster-Shafer theory of belief functions. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:259-269 Available from https://proceedings.mlr.press/v215/jirousek23a.html.

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