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Two Composition Operators for Belief Functions Revisited
 Jiroušek, Radim ; Kratochvíl, Václav ; Shenoy, P. P.
In probability theory, compositional models are as powerful as Bayesian networks. However, the relation between belief-function graphical models and the corresponding compositional models is much more complicated due to several reasons. One of them is that there are two composition operators for belief functions. This paper deals with their main properties and presents sufficient conditions under which they yield the same results.
Úplný záznam
Computing the Decomposable Entropy of Graphical Belief Function Models
 Jiroušek, Radim ; Kratochvíl, Václav ; Shenoy, P. P.
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.
Úplný záznam
A Note on Factorization of Belief Functions
 Jiroušek, Radim ; Shenoy, P. P.
The paper compares two main types of factorization of belief functions (one based on the Dempster´s rule of combination, the other based on the operator of composition) and shows that both the approaches are equivalent to each other in case of unconditional factorization and shows what are the differences when overlapping factorization is studied.
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