Computing the decomposable entropy of belief-function graphical models
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Issue Date
2023-07-13Author
Jiroušek, Radim
Kratochvíl, Václav
Shenoy, Prakash P.
Publisher
Elsevier
Type
Article
Article Version
Scholarly/refereed, publisher version
Rights
© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license.
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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.
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Citation
Jiroušek, R., Kratochvíl, V., Shenoy, P.P., (2023), Computing the decomposable entropy of belief-function graphical models, International Journal of Approximate Reasoning, vol. 161, 108984, https://doi.org/10.1016/j.ijar.2023.108984
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