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53
Bucket Elimination: A Unifying Framework for Probabilistic Inference
, 1996
"... . Probabilistic inference algorithms for belief updating, finding the most probable explanation, the maximum a posteriori hypothesis, and the maximum expected utility are reformulated within the bucket elimination framework. This emphasizes the principles common to many of the algorithms appearing ..."
Abstract

Cited by 293 (34 self)
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. Probabilistic inference algorithms for belief updating, finding the most probable explanation, the maximum a posteriori hypothesis, and the maximum expected utility are reformulated within the bucket elimination framework. This emphasizes the principles common to many of the algorithms appearing in the probabilistic inference literature and clarifies the relationship of such algorithms to nonserial dynamic programming algorithms. A general method for combining conditioning and bucket elimination is also presented. For all the algorithms, bounds on complexity are given as a function of the problem's structure. 1. Overview Bucket elimination is a unifying algorithmic framework that generalizes dynamic programming to accommodate algorithms for many complex problemsolving and reasoning activities, including directional resolution for propositional satisfiability (Davis and Putnam, 1960), adaptive consistency for constraint satisfaction (Dechter and Pearl, 1987), Fourier and Gaussian el...
Bucket Elimination: A Unifying Framework for Reasoning
"... Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination ..."
Abstract

Cited by 278 (62 self)
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Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucketelimination algorithms. These include: belief updating, finding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees; all are time and space exponential in the inducedwidth of the problem's interaction graph. While elimination strategies have extensive demands on memory, a contrasting class of algorithms called "conditioning search" require only linear space. Algorithms in this class split a problem into subproblems by instantiating a subset of variables, called a conditioning set, or a cutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization). The paper presents the bucketelimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade space for time.
Exploiting Causal Independence in Bayesian Network Inference
 Journal of Artificial Intelligence Research
, 1996
"... A new method is proposed for exploiting causal independencies in exact Bayesian network inference. ..."
Abstract

Cited by 157 (9 self)
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A new method is proposed for exploiting causal independencies in exact Bayesian network inference.
Inference in belief networks: A procedural guide
 International Journal of Approximate Reasoning
, 1996
"... Belief networks are popular tools for encoding uncertainty in expert systems. These networks rely on inference algorithms to compute beliefs in the context of observed evidence. One established method for exact inference onbelief networks is the Probability Propagation in Trees of Clusters (PPTC) al ..."
Abstract

Cited by 149 (6 self)
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Belief networks are popular tools for encoding uncertainty in expert systems. These networks rely on inference algorithms to compute beliefs in the context of observed evidence. One established method for exact inference onbelief networks is the Probability Propagation in Trees of Clusters (PPTC) algorithm, as developed byLauritzen and Spiegelhalter and re ned by Jensen et al. [1, 2, 3] PPTC converts the belief network into a secondary structure, then computes probabilities by manipulating the secondary structure. In this document, we provide a selfcontained, procedural guide to understanding and implementing PPTC. We synthesize various optimizations to PPTC that are scattered throughout the literature. We articulate undocumented, \open secrets " that are vital to producing a robust and e cient implementation of PPTC. We hope that this document makes probabilistic inference more accessible and a ordable to those without extensive prior exposure.
Multiply sectioned bayesian networks and junction forests for large knowledge based systems
 Computational Intelligence
, 1993
"... Abstract — We extend lazy propagation for inference in singleagent Bayesian networks to multiagent lazy inference in multiply sectioned Bayesian networks (MSBNs). Two methods are proposed using distinct runtime structures. We prove that the new methods are exact and efficient when domain structure ..."
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Cited by 79 (28 self)
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Abstract — We extend lazy propagation for inference in singleagent Bayesian networks to multiagent lazy inference in multiply sectioned Bayesian networks (MSBNs). Two methods are proposed using distinct runtime structures. We prove that the new methods are exact and efficient when domain structure is sparse. Both improve space and time complexity than the existing method, which allow multiagent probabilistic reasoning to be performed in much larger domains given the computational resource. Relative performance of the three methods are compared analytically and experimentally. I.
Probabilistic partial evaluation: exploiting rule structure in probabilistic inference
, 1997
"... Bayesian belief networks have grown to prominence because they provide compact representations of many domains, and there are algorithms to exploit this compactness. The next step is to allow compact representations of the conditional probability tables of a variable given its parents. In this paper ..."
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Cited by 39 (6 self)
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Bayesian belief networks have grown to prominence because they provide compact representations of many domains, and there are algorithms to exploit this compactness. The next step is to allow compact representations of the conditional probability tables of a variable given its parents. In this paper we present such a representation in terms of parent contexts and provide an algorithm that exploits this compactness. The representation is in terms of rules that provide conditional probabilities in different contexts. The algorithm is based on eliminating the variables not needed in an answer in turn. The operations for eliminating a variable correspond to a form of partial evaluation, where we are careful to maintain the probabilistic dependencies necessary for correct probabilistic inference. We show how this new method can exploit more structure than previous methods for structured belief network inference. 1
Lazy Propagation in Junction Trees
 In Proc. 14th Conf. on Uncertainty in Artificial Intelligence
, 1998
"... The efficiency of algorithms using secondary structures for probabilistic inference in Bayesian networks can be improved by exploiting independence relations induced by evidence and the direction of the links in the original network. In this paper we present an algorithm that exploits the independen ..."
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Cited by 36 (8 self)
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The efficiency of algorithms using secondary structures for probabilistic inference in Bayesian networks can be improved by exploiting independence relations induced by evidence and the direction of the links in the original network. In this paper we present an algorithm that exploits the independences relations induced by evidence and the direction of the links in the original network to reduce both time and space costs. Instead of multiplying the conditional probability distributions for the various cliques, we store a script specifying which potentials to multiply when a message is to be produced. The performance improvement of the algorithm is emphasized through empirical evaluations involving large real world Bayesian networks, and we compare the method with the Hugin and ShaferShenoy inference algorithms. 1 Introduction It has for a long time been a puzzle why "standard" inference algorithms for Bayesian networks did not really use the direction of the links in the network. By ...
Adaptive Assessment using Granularity Hierarchies and Bayesian Nets
, 1996
"... . Adaptive testing is impractical in real world situations where many different learner traits need to be measured in a single test. Recent student modelling approaches have attempted to solve this problem using different course representations along with sound knowledge propagation schemes. Thi ..."
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Cited by 34 (1 self)
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. Adaptive testing is impractical in real world situations where many different learner traits need to be measured in a single test. Recent student modelling approaches have attempted to solve this problem using different course representations along with sound knowledge propagation schemes. This paper shows that these different representations can be merged together and realized in a granularity hierarchy. Bayesian inference can be used to propagate knowledge throughout the hierarchy. This provides information for selecting appropriate test items and maintains a measure of the student's knowledge level. 1 Introduction Much of the previous work in computer adaptive testing has been concerned with testing a single, atomic learner trait [9, 8]. This approach needs to be extended to be considered useful in the intelligent tutoring systems field. Recent research in student modelling has attempted to allow testing of multiple learner traits in one model [2, 7, 6, 3, 1]. Each of th...
A Survey of Algorithms for RealTime Bayesian Network Inference
 In In the joint AAAI02/KDD02/UAI02 workshop on RealTime Decision Support and Diagnosis Systems
, 2002
"... As Bayesian networks are applied to more complex and realistic realworld applications, the development of more efficient inference algorithms working under realtime constraints is becoming more and more important. This paper presents a survey of various exact and approximate Bayesian network ..."
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Cited by 32 (2 self)
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As Bayesian networks are applied to more complex and realistic realworld applications, the development of more efficient inference algorithms working under realtime constraints is becoming more and more important. This paper presents a survey of various exact and approximate Bayesian network inference algorithms. In particular, previous research on realtime inference is reviewed. It provides a framework for understanding these algorithms and the relationships between them. Some important issues in realtime Bayesian networks inference are also discussed.
Partial abductive inference in Bayesian belief networks using a genetic algorithm
 Pattern Recognit. Lett
, 1999
"... Abstract—Abductive inference in Bayesian belief networks (BBNs) is intended as the process of generating the most probable configurations given observed evidence. When we are interested only in a subset of the network’s variables, this problem is called partial abductive inference. Both problems are ..."
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Cited by 24 (2 self)
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Abstract—Abductive inference in Bayesian belief networks (BBNs) is intended as the process of generating the most probable configurations given observed evidence. When we are interested only in a subset of the network’s variables, this problem is called partial abductive inference. Both problems are NPhard and so exact computation is not always possible. In this paper, a genetic algorithm is used to perform partial abductive inference in BBNs. The main contribution is the introduction of new genetic operators designed specifically for this problem. By using these genetic operators, we try to take advantage of the calculations previously carried out, when a new individual is evaluated. The algorithm is tested using a widely used Bayesian network and a randomly generated one and then compared with a previous genetic algorithm based on classical genetic operators. From the experimental results, we conclude that the new genetic operators preserve the accuracy of the previous algorithm, and also reduce the number of operations performed during the evaluation of individuals. The performance of the genetic algorithm is, thus, improved. Index Terms—Abductive inference, bayesian belief networks, evolutionary computation, genetic operators, most probable explanation, probabilistic reasoning. I.