Join tree propagation utilizing both arc reversal and variable elimination

Butz, Cory J.; Konkel, K.; Lingras, Pawan

doi:10.1016/j.ijar.2010.11.006

Cited by 11 publications

(8 citation statements)

References 17 publications

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“…Here, X and E are disjoint subsets of U , and E is observed taking value e. We describe a basic algorithm for computing p(X|E = e), called variable elimination (VE), first put forth in [17]. We do not consider alternative approaches to inference such as conditioning [6] and join tree propagation [1,2,10]. Inference involves the elimination of variables.…”

Section: Inferencementioning

confidence: 99%

See 1 more Smart Citation

d-Separation: Strong Completeness of Semantics in Bayesian Network Inference

Butz¹,

Yan²,

Madsen

2013

Advances in Artificial Intelligence

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Abstract. It is known that d-separation can determine the minimum amount of information needed to process a query during exact inference in discrete Bayesian networks. Unfortunately, no practical method is known for determining the semantics of the intermediate factors constructed during inference. Instead, all inference algorithms are relegated to denoting the inference process in terms of potentials. In this theoretical paper, we give an algorithm, called Semantics in Inference (SI), that uses d-separation to denote the semantics of every potential constructed during inference. We show that SI possesses four salient features: polynomial time complexity, soundness, completeness, and strong completeness. SI provides a better understanding of the theoretical foundation of Bayesian networks and can be used for improved clarity, as shown via an examination of Bayesian network literature.

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Section: Inferencementioning

confidence: 99%

“…For example, consider potential ψ(g, i = 1, j) in (2). F (ψ(g, i = 1, j)), the evidence expanded form, can be easily obtained in a recursive manner as follows:…”

Section: Understanding Semanticsmentioning

confidence: 99%

d-Separation: Strong Completeness of Semantics in Bayesian Network Inference

Butz¹,

Yan²,

Madsen

2013

Advances in Artificial Intelligence

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“…Several exact 2,3,4,5,6,7,8 and approximate 9,10,11,12,13 inference algorithms can be found in the literature, due to the fact that it is an NP-hard problem, 14,15 which justifies the study of new techniques and algorithms with the aim of widening the class of affordable problems. Some of the most relevant inference algorithms incorporate the ability of dealing with factorised representations of the potentials that represent the probabilistic information.…”

Section: Bayesian Networkmentioning

confidence: 99%

Fast Factorisation of Probabilistic Potentials and Its Application to Approximate Inference in Bayesian Networks

Cano

Gómez-Olmedo

Pérez-Ariza

et al. 2012

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

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We present an efficient procedure for factorising probabilistic potentials represented as probability trees. This new procedure is able to detect some regularities that cannot be captured by existing methods. In cases where an exact decomposition is not achievable, we propose a heuristic way to carry out approximate factorisations guided by a parameter called factorisation degree, which is fast to compute. We show how this parameter can be used to control the tradeoff between complexity and accuracy in approximate inference algorithms for Bayesian networks.

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“…A review of recent literature shows the variety of applications in which they have been successfully used [1,10,24,35,45]. One of the main reasons for using them as the inference engine in a decision support system is that efficient reasoning algorithms can be designed, taking advantage of their structure [2,3,16,44,43,30,29].…”

Section: Introductionmentioning

confidence: 99%