Importance sampling algorithms for the propagation of probabilities in belief networks

Cano, José; Hernández, Luís; Moral, Serafı́n

doi:10.1016/0888-613x(96)00013-8

Cited by 14 publications

(25 citation statements)

References 6 publications

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“…First-order reliability method (FORM) (Allen and Camberos, 2009), second-order reliability method (SORM) (Allen and Camberos, 2009), importance sampling method (Cano et al, 1996), and MCS are a short list of available methods. Except for MCS, all other methods use approximation in either output variable or its distribution, which inevitably involves error especially when the governing system equation is complex.…”

Section: Surrogate Modeling -Cross-validationmentioning

confidence: 99%

Uncertainty analysis for rolling contact fatigue failure probability of silicon nitride ball bearings

Pattabhiraman

Levesque

Kim

et al. 2010

International Journal of Solids and Structures

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Section: Surrogate Modeling -Cross-validationmentioning

confidence: 99%

Uncertainty analysis for rolling contact fatigue failure probability of silicon nitride ball bearings

Pattabhiraman

Levesque

Kim

et al. 2010

International Journal of Solids and Structures

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“…The former is related to the exponential number of parameters required to fill the conditional probability table (CPT) of a variable while the latter is related to the non-polynomial time required to do belief updating in a BN [8]. Different schemes and approximate/simulation-based algorithms have been suggested that aim to tackle the belief updating issue [1,7,[12][13][14]29]. For knowledge elicitation, schemes such as Noisy-Or [27,28] and the CAST logic [6,29] have been proposed that ask a linear number of parameters from a subject matter expert and convert them into conditional probability tables (having exponential number of parameters).…”

Section: Introductionmentioning

confidence: 99%

Complexity reduction of influence nets using arc removal

Haider

Raza

2015

Journal of Intelligent &Amp; Fuzzy Systems

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The model building of Influence Nets, a special instance of Bayesian belief networks, is a time-consuming and laborintensive task. No formal process exists that decision makers/system analyst, who are typically not familiar with the underlying theory and assumptions of belief networks, can use to build concise and easy-to-interpret models. In many cases, the developed model is extremely dense, that is, it has a very high link-to-node ratio. The complexity of a network makes the already intractable task of belief updating more difficult. The problem is further intensified in dynamic domains where the structure of the built model is repeated for multiple time-slices. It is, therefore, desirable to do a post-processing of the developed models and to remove arcs having a negligible influence on the variable(s) of interests. The paper applies sensitivity of arc analysis to identify arcs that can be removed from an Influence Net without having a significant impact on its inferencing capability. A metric is suggested to gauge changes in the joint distribution of variables before and after the arc removal process. The results are benchmarked against the KL divergence metric. An empirical study based on several real Influence Nets is conducted to test the performance of the sensitivity of arc analysis in reducing the model complexity of an Influence Net without causing a significant change in its joint probability distribution.

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“…Known importance sampling algorithms, as those developed by Cano et al (1996);Fung and Chang (1990); Shachter and Peot (1990) and Dagum and Luby (1997) generate conÿgurations simulating values for each non-observed variable using its conditional distribution, and instantiating each observed variable in X E to the evidence e. This may lead to bad situations. This happens when most of the weights are low and a few of them are high.…”

Section: Computing a Sampling Distributionmentioning

confidence: 99%

“…If we want to calculate the 'a posteriori' probability for all the variables in the network, then for each case of each variable, a sampling distribution has to be computed and a sample drawn from it. This is the solution adopted in Cano et al (1996). Dagum and Luby (1997) use a slightly di erent method; they estimate p(x k ; e) and p(e) with di erent samples in order to obtain and approximation for p(x k |e).…”

Section: Importance Sampling In Bayesian Networkmentioning

confidence: 99%

Importance sampling in Bayesian networks using probability trees

Salmerón

Cano

Moral

2000

Computational Statistics & Data Analysis

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In this paper a new Monte-Carlo algorithm for the propagation of probabilities in Bayesian networks is proposed. This algorithm has two stages: in the ÿrst one an approximate propagation is carried out by means of a deletion sequence of the variables. In the second stage a sample is obtained using as sampling distribution the calculations of the ÿrst step. The di erent conÿgurations of the sample are weighted according to the importance sampling technique. We show how the use of probability trees to store and to approximate probability potentials, and a careful selection of the deletion sequence, make this algorithm able to propagate over large networks with extreme probabilities.

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Importance sampling algorithms for the propagation of probabilities in belief networks

Cited by 14 publications

References 6 publications

Uncertainty analysis for rolling contact fatigue failure probability of silicon nitride ball bearings

Uncertainty analysis for rolling contact fatigue failure probability of silicon nitride ball bearings

Complexity reduction of influence nets using arc removal

Importance sampling in Bayesian networks using probability trees

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