Belief function independence: I. The marginal case

Yaghlane, Boutheina Ben; Smets, Philippe; Mellouli, Khaled

doi:10.1016/s0888-613x(01)00055-x

Cited by 47 publications

(25 citation statements)

References 7 publications

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“…However, the concept of cognitive independence does not inherit all of the properties of the probabilistic notion of independence and may be seen as a weak form of independence. See [34,35] for an in-depth analysis of independence concepts in the belief function theory.…”

Section: Independencementioning

confidence: 99%

Learning from partially supervised data using mixture models and belief functions

Côme

Oukhellou

Denux

et al. 2009

Pattern Recognition

108

110

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This paper addresses classification problems in which the class membership of training data is only partially known. Each learning sample is assumed to consist in a feature vector xi ∈ X and an imprecise and/or uncertain "soft" label mi defined as a Dempster-Shafer basic belief assignment over the set of classes. This framework thus generalizes many kinds of learning problems including supervised, unsupervised and semi-supervised learning. Here, it is assumed that the feature vectors are generated from a mixture model. Using the Generalized Bayesian Theorem, an extension of Bayes' theorem in the belief function framework, we derive a criterion generalizing the likelihood function. A variant of the EM algorithm dedicated to the optimization of this criterion is proposed, allowing us to compute estimates of model parameters. Experimental results demonstrate the ability of this approach to exploit partial information about class labels.

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Section: Independencementioning

confidence: 99%

Learning from partially supervised data using mixture models and belief functions

Côme

Oukhellou

Denux

et al. 2009

Pattern Recognition

108

110

View full text Add to dashboard Cite

show abstract

“…The work benefits from the efforts that have already been done to formalize theoretically the distinct concepts of independence that arise in problems involving both variability and imprecision, [70][71][72] within the frameworks of both evidence [73][74][75][76] and possibility theories. [77][78][79][80][81] The practical implications of different definitions of independence are illustrated with reference to the probabilistic risk assessment of engineering systems by Refs.…”

Section: -62mentioning

confidence: 99%

Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Pedroni

Zio

2012

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Risk analysis models describing aleatory (i.e., random) events contain parameters (e.g., probabilities, failure rates, …) that are epistemically-uncertain, i.e., known with poor precision. Whereas aleatory uncertainty is always described by probability distributions, epistemic uncertainty may be represented in different ways (e.g., probabilistic or possibilistic), depending on the information and data available. The work presented in this paper addresses the issue of accounting for (in)dependence relationships between epistemically-uncertain parameters. When a probabilistic representation of epistemic uncertainty is considered, uncertainty propagation is carried out by a two-dimensional (or double) Monte Carlo (MC) simulation approach; instead, when possibility distributions are used, two approaches are undertaken: the hybrid MC and Fuzzy Interval Analysis (FIA) method and the MCbased Dempster-Shafer (DS) approach employing Independent Random Sets (IRSs). The objectives are: i) studying the effects of (in)dependence between the epistemically-uncertain parameters of the aleatory probability distributions (when a probabilistic/possibilistic representation of epistemic uncertainty is adopted) and ii) studying the effect of the probabilistic/possibilistic representation of epistemic uncertainty (when the state of dependence between the epistemic parameters is defined). The Dependency Bound Convolution (DBC) approach is then undertaken within a hierarchical setting of hybrid (probabilistic and possibilistic) uncertainty propagation, in order to account for all kinds of (possibly unknown) dependences between the random variables. The analyses are carried out with reference to two toy examples, built in such a way to allow performing a fair quantitative comparison between the methods, and evaluating their rationale and appropriateness in relation to risk analysis.

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“…It is, perhaps, also necessary to stress that the operator of composition is something other than the famous Dempster's rule of combination [6], or its non-normalised version, the so called conjunctive combination rule [2] (m 1 ∩ m 2 )(C) =…”

Section: Remarkmentioning

confidence: 99%

Local computations in Dempster–Shafer theory of evidence

Jiroušek

2012

International Journal of Approximate Reasoning

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When applying any technique of multidimensional models to problems of practice, one always has to cope with two problems: the necessity to represent the models with a "reasonable" number of parameters and to have sufficiently efficient computational procedures at one's disposal. When considering graphical Markov models in probability theory, both of these conditions are fulfilled; various computational procedures for decomposable models are based on the ideas of local computations, whose theoretical foundations were laid by Lauritzen and Spiegelhalter.The presented contribution studies a possibility of transferring these ideas from probability theory into Dempster-Shafer theory of evidence. The paper recalls decomposable models, discusses connection of the model structure with the corresponding system of conditional independence relations, and shows that under special additional conditions, one can locally compute specific basic assignments which can be considered to be conditional.

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Belief function independence: I. The marginal case

Cited by 47 publications

References 7 publications

Learning from partially supervised data using mixture models and belief functions

Learning from partially supervised data using mixture models and belief functions

Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Local computations in Dempster–Shafer theory of evidence

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