Computing the Decomposable Entropy of Graphical Belief Function Models

0558135 - ÚTIA 2023 RIV CZ eng K - Konferenční příspěvek (tuzemská konf.)
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]
Grant CEP: GA ČR(CZ) GA19-04579S
Grant ostatní: GA ČR(CZ) GA19-06569S
Program: GA
Institucionální podpora: RVO:67985556
Klíčová slova: Decomposable Entropy * DempsterShafer belief functions * Bayesian networks
Obor OECD: 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.
Trvalý link: http://hdl.handle.net/11104/0332321