Computing the Decomposable Entropy of Graphical Belief Function Models

0558135 - ÚTIA 2023 RIV CZ eng K - Conference Paper (Czech conference)
Jiroušek, Radim - Kratochvíl, Václav - Shenoy, P. P.
Computing the Decomposable Entropy of Graphical Belief Function Models.
Proceedings of the 12th Workshop on Uncertainty Processing. Prague: MatfyzPress, 2022 - (Studený, M.; Ay, N.; Coletti, G.; Kleiter, G.; Shenoy, P.), s. 111-122. ISBN 978-80-7378-460-7.
[WUPES 2022: 12th Workshop on Uncertainty Processing. Kutná Hora (CZ), 01.06.2022-04.06.2022]
R&D Projects: GA ČR(CZ) GA19-04579S
Grant - others:GA ČR(CZ) GA19-06569S
Program: GA
Institutional support: RVO:67985556
Keywords : Decomposable Entropy * DempsterShafer belief functions * Bayesian networks
OECD category: Applied mathematics
http://library.utia.cas.cz/separaty/2022/MTR/kratochvil-0558135.pdf

In 2018, Jiroušek and Shenoy proposed a definition of entropy for Dempster-Shafer (D-S) belief functions called decomposable entropy. Here, we provide an algorithm for computing the decomposable entropy of directed graphical D-S belief function models. For undirected graphical belief function models, assuming that each belief function in the model is non-informative to the others, no algorithm is necessary. We compute the entropy of each belief function and add them together to get the decomposable entropy of the model. Finally, the decomposable entropy generalizes Shannon’s entropy not only for the probability of a single random variable but also for multinomial distributions expressed as directed acyclic graphical models called Bayesian networks.
Permanent Link: http://hdl.handle.net/11104/0332321