Gaussian Influence Diagrams

Shachter, Ross D.; Kenley, C. Robert

doi:10.1287/mnsc.35.5.527

Cited by 309 publications

(249 citation statements)

References 11 publications

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“…Barren variables can be exploited in inference [7]. A variable is barren [13], if it is neither an evidence nor a target variable and it only has barren descendants. Probabilistic inference can be conducted directly in the original BN [6,9,12,13,17,18,19].…”

Section: Probabilistic Inferencementioning

confidence: 99%

“…A variable is barren [13], if it is neither an evidence nor a target variable and it only has barren descendants. Probabilistic inference can be conducted directly in the original BN [6,9,12,13,17,18,19]. It can also be performed in a join tree [3,5,7,8,14].…”

Section: Probabilistic Inferencementioning

confidence: 99%

“…A second approach to BN inference is direct computation (DC), which performs inference directly in a BN. The classical DC algorithms are variable elimination (VE) [17,18,19], arc-reversal (AR) [9,13] and symbolic probabilistic inference (SPI) [6,12]. The experimental results provided by Zhang [17] indicate that VE is more efficient than the classical JTP methods when updating twenty or less non-evidence variables, given a set of twenty or fewer evidence variables.…”

Section: Introductionmentioning

confidence: 99%

“…When a JT node is ready to send its CPT messages to a neighbour, the LAZY-AR approach eliminates all variables not appearing in the neighbour node. In particular, eliminating variable v may require directed edges (arcs) to be reversed in the DAG (defined by the CPTs at the sending JT node) in order to make v barren [13]. Such arc reversals are useful, since it is well-known that barren variables can be exploited for more efficient inference [7].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Improved LAZY-AR Approach to Bayesian Network Inference

Butz

Song

2006

Advances in Artificial Intelligence

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Abstract. We propose LAZY arc-reversal with variable elimination (LAZY-ARVE) as a new approach to probabilistic inference in Bayesian networks (BNs). LAZY-ARVE is an improvement upon LAZY arcreversal (LAZY-AR), which was very recently proposed and empirically shown to be the state-of-the-art method for exact inference in discrete BNs. The primary advantage of LAZY-ARVE over LAZY-AR is that the former only computes the actual distributions passed during inference, whereas the latter may perform unnecessary computation by constructing irrelevant intermediate distributions. A comparison between LAZY-AR and LAZY-ARVE, involving processing evidence in a real-world BN for coronary heart disease, is favourable towards LAZY-ARVE.

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Section: Probabilistic Inferencementioning

confidence: 99%

Section: Probabilistic Inferencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Improved LAZY-AR Approach to Bayesian Network Inference

Butz

Song

2006

Advances in Artificial Intelligence

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“…The irrelevant variables include barren variables [13] and d-separated variables [5]. Barren variables are variables whose marginalization would produce intermediate distributions full of 1s.…”

Section: Relevant Variablesmentioning

confidence: 99%

Exploiting Dynamic Independence in a Static Conditioning Graph

Grant

Horsch

2006

Advances in Artificial Intelligence

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Abstract. A conditioning graph (CG) is a graphical structure that attempt to minimize the implementation overhead of computing probabilities in belief networks. A conditioning graph recursively factorizes the network, but restricting each decomposition to a single node allows us to store the structure with minimal overhead, and compute with a simple algorithm. This paper extends conditioning graphs with optimizations that effectively reduce the height of the CG, thus reducing time complexity exponentially, while increasing the storage requirements by only a constant factor. We conclude that CGs are frequently as efficient as any other exact inference method, with the advantage of being vastly superior to VE and JT in terms of space complexity, and far simpler to implement.

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A simulator for evaluating methods for the detection of lesion-deficit associations

Megalooikonomou¹,

Davatzikos²,

Herskovits³

2000

Hum. Brain Mapp.

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Although much has been learned about the functional organization of the human brain through lesion-deficit analysis, the variety of statistical and image-processing methods developed for this purpose precludes a closed-form analysis of the statistical power of these systems. Therefore, we developed a lesion-deficit simulator (LDS), which generates artificial subjects, each of which consists of a set of functional deficits, and a brain image with lesions; the deficits and lesions conform to predefined distributions. We used probability distributions to model the number, sizes, and spatial distribution of lesions, to model the structure-function associations, and to model registration error. We used the LDS to evaluate, as examples, the effects of the complexities and strengths of lesion-deficit associations, and of registration error, on the power of lesion-deficit analysis. We measured the numbers of recovered associations from these simulated data, as a function of the number of subjects analyzed, the strengths and number of associations in the statistical model, the number of structures associated with a particular function, and the prior probabilities of structures being abnormal. The number of subjects required to recover the simulated lesion-deficit associations was found to have an inverse relationship to the strength of associations, and to the smallest probability in the structure-function model. The number of structures associated with a particular function (i.e., the complexity of associations) had a much greater effect on the performance of the analysis method than did the total number of associations. We also found that registration error of 5 mm or less reduces the number of associations discovered by approximately 13% compared to perfect registration. The LDS provides a flexible framework for evaluating many aspects of lesion-deficit analysis.

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Gaussian Influence Diagrams

Cited by 309 publications

References 11 publications

An Improved LAZY-AR Approach to Bayesian Network Inference

An Improved LAZY-AR Approach to Bayesian Network Inference

Exploiting Dynamic Independence in a Static Conditioning Graph

A simulator for evaluating methods for the detection of lesion-deficit associations

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