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Keywords
(3)
Conditional Independence
Evidence Theory
Possibility Theory
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Compositional models and conditional independence in evidence theory
Compositional models and conditional independence in evidence theory,10.1016/j.ijar.2010.02.005,International Journal of Approximate Reasoning,Radim J
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Compositional models and conditional independence in evidence theory
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Citations: 3
)
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Radim Jirousek
,
Jirina Vejnarová
The goal of the paper is twofold. The first is to show that some of the ideas for representation of multidimensional distributions in probability and possibility theories can be transferred into evidence theory. Namely, we show that multidimensional basic assignments can be rather efficiently represented in a form of socalled compositional models. These models are based on the iterative application of the operator of composition, whose definition for basic assignments as well as its properties are presented. We also prove that the operator of composition in
evidence theory
is in a sense generalization of its probabilistic counterpart.The second goal of the paper is to introduce a new definition of
conditional independence
in
evidence theory
and to show in what sense it is superior to that formerly introduced by other authors.
Journal:
International Journal of Approximate Reasoning  IJAR
, vol. 52, no. 3, pp. 316334, 2011
DOI:
10.1016/j.ijar.2010.02.005
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Citation Context
(3)
...Our approach is based on previously introduced operator of composition for basic assignments [7,
6
]. The evidential network is reconstructed from the resulting compositional model...
...In this paper we will use the concept introduced in [11,
6
], as we consider it more suitable (the arguments can be found in [11])...
...A lot of other properties possessed by the operator of composition can be found in [
6
, 7], nevertheless here we will confine ourselves to the following theorem (proven in [6]) expressing the relationship between conditional independence and operator of composition...
...A lot of other properties possessed by the operator of composition can be found in [6, 7], nevertheless here we will confine ourselves to the following theorem (proven in [
6
]) expressing the relationship between conditional independence and operator of composition...
...The property explaining why we call these sequences “perfect” is expressed by the following assertion proven in [
6
]...
Jiřina Vejnarová
.
An Alternative Approach to Evidential Network Construction
...Here, we will use another (and as it was showed in [
6
] still equivalent) definition...
...[2, 10, 12]) but the following definition introduced in [
6
]...
Radim Jiroušek
.
An Attempt to Define Graphical Models in DempsterShafer Theory of Evi...
...In [8,
7
] we proved a number of properties concerning the operator of composition; the following ones are the most important for the purpose of this paper...
Radim Jiroušek
.
Belief Networks and Local Computations
References
(13)
Conditional independence structure and its closure: Inferential rules and algorithms
(
Citations: 7
)
Marco Baioletti
,
Giuseppe Busanello
,
Barbara Vantaggi
Journal:
International Journal of Approximate Reasoning  IJAR
, vol. 50, no. 7, pp. 10971114, 2009
On the Desirability of Acyclic Database Schemes
(
Citations: 359
)
Catriel Beeri
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Ronald Fagin
,
David Maier
,
Mihalis Yannakakis
Journal:
Journal of The ACM  JACM
, vol. 30, no. 3, pp. 479513, 1983
Inference in directed evidential networks based on the transferable belief model
(
Citations: 10
)
Boutheina Ben Yaghlane
,
Khaled Mellouli
Journal:
International Journal of Approximate Reasoning  IJAR
, vol. 48, no. 2, pp. 399418, 2008
A survey of concepts of independence for imprecise probabilities
(
Citations: 71
)
INES COUSO
,
SERAFIN MORAL
,
PETER WALLEY
Journal:
Risk Decision and Policy
, vol. 5, no. 2, pp. 165181, 2000
$I$Divergence Geometry of Probability Distributions and Minimization Problems
(
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I. Csiszar
Journal:
Annals of Probability  ANN PROBAB
, vol. 3, no. 1975, pp. 146158, 1975
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Citations
(3)
An Alternative Approach to Evidential Network Construction
Jiřina Vejnarová
An Attempt to Define Graphical Models in DempsterShafer Theory of Evidence
Radim Jiroušek
Belief Networks and Local Computations
Radim Jiroušek