Computing the decomposable entropy of belief-function graphical models

0573803 - ÚTIA 2024 RIV US eng J - Článek v odborném periodiku
Jiroušek, Radim - Kratochvíl, Václav - Shenoy, P. P.
Computing the decomposable entropy of belief-function graphical models.
International Journal of Approximate Reasoning. Roč. 161, č. 1 (2023), č. článku 108984. ISSN 0888-613X. E-ISSN 1873-4731.
[The 12th Workshop on Uncertainty Processing. Kutná Hora, 01.06.2022-04.06.2022]
Grant CEP: GA ČR(CZ) GA21-07494S
Institucionální podpora: RVO:67985556
Klíčová slova: Dempster-Shafer theory of belief functions * Decomposable entropy * Belief-function directed graphical models * Belief-function undirected graphical models
Obor OECD: Applied mathematics
Impakt faktor: 3.9, rok: 2022
Způsob publikování: Open access
http://library.utia.cas.cz/separaty/2023/MTR/jirousek-0573803.pdf https://www.sciencedirect.com/science/article/pii/S0888613X23001159?via%3Dihub

In 2018, Jiroušek and Shenoy proposed a definition of entropy for Dempster-Shafer (D-S) belief functions called decomposable entropy (d-entropy). This paper provides an algorithm for computing the d-entropy of directed graphical D-S belief function models. We illustrate the algorithm using Almond's Captain's Problem example. For belief function undirected graphical models, assuming that the set of belief functions in the model is non-informative, the belief functions are distinct. We illustrate this using Haenni-Lehmann's Communication Network problem. As the joint belief function for this model is quasi-consonant, it follows from a property of d-entropy that the d-entropy of this model is zero, and no algorithm is required. For a class of undirected graphical models, we provide an algorithm for computing the d-entropy of such models. Finally, the d-entropy coincides with Shannon's entropy for the probability mass function of a single random variable and for a large multi-dimensional probability distribution expressed as a directed acyclic graph model called a Bayesian network. We illustrate this using Lauritzen-Spiegelhalter's Chest Clinic example represented as a belief-function directed graphical model.
Trvalý link: https://hdl.handle.net/11104/0344420