Axioms for Probability and Belief-Function Propagation

Shenoy, Prakash P.; Shafer, Glenn

doi:10.1016/b978-0-444-88650-7.50019-6

Cited by 216 publications

(151 citation statements)

References 17 publications

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“…the network structures they support, but in most cases they are applicable independent of the given uncertainty calculus, provided, of course, the elementary operations like extension (conditioning) and projection have been adapted to this calculus [33,35,44]. A fairly general approach to reasoning under uncertainty in so-called valuation-based networks has been proposed in [46,48,47]. It can be applied, for example, to upper and lower probabilities [52], Dempster-Shafer theory of evidence [12,13,42,43,49], and possibility theory [56,15,16], and has been implemented in the software tool PULCINELLA [41].…”

Section: Evidence Propagationmentioning

confidence: 99%

“…An important method to represent the resulting decomposition is graphical modeling. It also provides useful theoretical and practical concepts for efficient reasoning under uncertainty [54,6,35,48]. Applications of graphical models can be found in a large variety of areas including diagnostics, expert systems, planning, data analysis, and control.…”

Section: Introductionmentioning

confidence: 99%

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Possibilistic Graphical Models

Borgelt

Gebhardt

Kruse

2000

Computational Intelligence in Data Mining

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Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledge-based systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning, which have been well-known for over ten years now. However, they suffer from certain deficiencies, if imprecise information has to be taken into account. Therefore possibilistic graphical modeling has recently emerged as a promising new area of research. Possibilistic networks are a noteworthy alternative to probabilistic networks whenever it is necessary to model both uncertainty and imprecision. Imprecision, understood as set-valued data, has often to be considered in situations in which information is obtained from human observers or imprecise measuring instruments. In this paper we provide an overview on the state of the art of possibilistic networks w.r.t. to propagation and learning algorithms.

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Section: Evidence Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Possibilistic Graphical Models

Borgelt

Gebhardt

Kruse

2000

Computational Intelligence in Data Mining

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“…One limitation of the variable elimination algorithm, as formulated above, is that it has to be repeated for each variable of interest. This is overcome in other inference algorithms, e.g., [19].…”

Section: Inferencementioning

confidence: 99%

Inference in hybrid Bayesian networks

Langseth

Nielsen

Rumí

et al. 2009

Reliability Engineering & System Safety

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a b s t r a c tSince the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs' calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.

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“…It is well known that the exact inference schemes currently employed (e.g., [1]) only work for some particular classes of hybrid BNs. The most common strategies for performing inference in a hybrid BN can roughly be divided into three categories: Firstly, a subset of models (commonly referred to conditional Gaussian models) allow exact inference.Secondly, approximate inference procedures like stochastic sampling can be employed.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, though, this algorithm has computational issues, which have prevented it from being commonly used in practice. 1 For instance, the algorithm requires re-implementation of the message passing algorithm for inference (communicating objects called "weights", which are used to re-adjust the discretisation when evidence is found in low-probability regions of the density together with the standard messages), it uses specialised data structures called binary split partition trees for which the standard inference operations must be defined, and it must find or approximate the minimum and maximum values of potentially high-dimensional functions on each hypercube to utilise the bound in Equation (2).…”

Section: Introductionmentioning

confidence: 99%

Fast Approximate Inference in Hybrid Bayesian Networks Using Dynamic Discretisation

Langseth

Márquez

Neil

2013

Natural and Artificial Models in Computation and Biology

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Abstract. We consider inference in a Bayesian network that can consist of a mix of discrete and continuos variables. It is well known that this is a task that cannot be solved in general using a standard inference algorithms based on the junction-tree. A common solution to this problem is to discretise the continuous variables to obtain a fully discrete model, in which standard inference can be performed. The most efficient discretisation procedure in terms of cost of inference is known as dynamic discretisation, and was published by Kozlov and Koller in the late 90's. In this paper we discuss an already published simplification to that algorithm by Neil et al. The simplification is in practise orders of magnitudes faster than Kozlov and Koller's technique, but potentially at the cost of some lack of precision. We consider the mathematical properties of Neil et al.'s algorithm, and challenge it by constructing models that are particularly difficult for that method. Some simple modifications to the core algorithm are proposed, and the empirical results are very promising, indicating that the simplified procedure is feasible also for very challenging problems.

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Axioms for Probability and Belief-Function Propagation

Cited by 216 publications

References 17 publications

Possibilistic Graphical Models

Possibilistic Graphical Models

Inference in hybrid Bayesian networks

Fast Approximate Inference in Hybrid Bayesian Networks Using Dynamic Discretisation

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