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

0573617 - ÚTIA 2024 RIV ES eng C - Konferenční příspěvek (zahraniční konf.)
Jiroušek, Radim - Kratochvíl, Václav - Shenoy, P. P.
On the relationship between graphical and compositional models for the Dempster-Shafer theory of belief functions.
Proceedings of Machine Learning Research, Volume 215: International Symposium on Imprecise Probability: Theories and Applications,. Almerı́a: PMLR, 2023, s. 259-269. E-ISSN 2640-3498.
[International Symposium on Imprecise Probability: Theories and Applications 2023 /13./. Oviedo (ES), 11.07.2023-14.07.2023]
Grant CEP: GA ČR(CZ) GA21-07494S
Institucionální podpora: RVO:67985556
Klíčová slova: joint belief functions * conditional independence * Markov models * composition operators * Dempster’s combination rule * conditionals
Obor OECD: Pure mathematics
http://library.utia.cas.cz/separaty/2023/MTR/jirousek-0573617.pdf

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.
Trvalý link: https://hdl.handle.net/11104/0345846