Ústav teorie informace a automatizace

Jste zde

Bibliografie

Journal Article

Computing the decomposable entropy of belief-function graphical models

Jiroušek Radim, Kratochvíl Václav, Shenoy P. P.

: International Journal of Approximate Reasoning vol.161, 108984

: The 12th Workshop on Uncertainty Processing, (Kutná Hora, CZ, 20220601)

: GA21-07494S, GA ČR

: Dempster-Shafer theory of belief functions, Decomposable entropy, Belief-function directed graphical models, Belief-function undirected graphical models

: 10.1016/j.ijar.2023.108984

: http://library.utia.cas.cz/separaty/2023/MTR/jirousek-0573803.pdf

: https://www.sciencedirect.com/science/article/pii/S0888613X23001159?via%3Dihub

(eng): 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.

: BA

: 10102

07.01.2019 - 08:39