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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 ..."
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Cited by 294 (58 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.
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 in ..."
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Cited by 289 (27 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.
Learning Bayesian belief networks: An approach based on the MDL principle
 Computational Intelligence
, 1994
"... A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being lear ..."
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Cited by 247 (7 self)
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A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being learned. In particular, our method can learn unrestricted multiplyconnected belief networks. Furthermore, unlike other approaches our method allows us to tradeo accuracy and complexity in the learned model. This is important since if the learned model is very complex (highly connected) it can be conceptually and computationally intractable. In such a case it would be preferable to use a simpler model even if it is less accurate. The MDL principle o ers a reasoned method for making this tradeo. We also show that our method generalizes previous approaches based on Kullback crossentropy. Experiments have been conducted to demonstrate the feasibility of the approach. Keywords: Knowledge Acquisition � Bayes Nets � Uncertainty Reasoning. 1
A Recurrence Local Computation Approach Towards Ordering Composite Beliefs in Bayesian Belief Networks
, 1993
"... Finding the l Most Probable Explanations (MPE) of a given evidence, S e , in a Bayesian belief network can be formulated as identifying and ordering a set of composite hypotheses, H i s, of which the posterior probabilities are the l largest; i.e., P r(H 1 jS e ) ::: P r(H l jS e ). When an orde ..."
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Cited by 10 (5 self)
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Finding the l Most Probable Explanations (MPE) of a given evidence, S e , in a Bayesian belief network can be formulated as identifying and ordering a set of composite hypotheses, H i s, of which the posterior probabilities are the l largest; i.e., P r(H 1 jS e ) ::: P r(H l jS e ). When an order includes all the composite hypotheses in the network in order to find all the probable explanations, it becomes a total order and the derivation of such an order has an exponential complexity. The focus of this paper is on the derivation of a partial order, with length l, for finding the l most probable composite hypotheses; where l typically is much smaller than the total number of composite hypotheses in a network. Previously, only the partial order of length two (i.e., l = 2) in a singly connected Bayesian network could be efficiently derived without further restriction on network topologies and the increase in spatial complexity. This paper discusses an efficient algorithm for the deri...
A Dynamic Bayesian Network for Handling Uncertainty in a Decision Support System Adapted to the Monitoring of Patients Treated by Hemodialysis
 in &quot;17th IEEE International Conference on Tools with Artificial Intelligence  ICTAI’05, Hong Kong/China
, 2005
"... Telemedicine is a mean of facilitating the distribution of human resources and professional competences. It can speed up diagnosis and therapeutic care delivery and allow peripheral healthcare providers to receive continuous assistance from specialized centers. The need of specialized human resource ..."
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Cited by 4 (0 self)
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Telemedicine is a mean of facilitating the distribution of human resources and professional competences. It can speed up diagnosis and therapeutic care delivery and allow peripheral healthcare providers to receive continuous assistance from specialized centers. The need of specialized human resources becomes critical with the aging of the population. The treatment of renal failure is an example where telemedicine can help to increase care quality. Over the last decades Bayesian networks has become a popular representation for encoding uncertain expert knowledge. Dynamic Bayesian networks are an extension of Bayesian networks for modeling dynamic processes. We developed a dynamic Bayesian network adapted to the monitoring of the dry weight of patients suffering from chronic renal failure treated by hemodialysis. An experimentation conducted at dialysis units indicated that the system is reliable and gets the approbation of its users. 1.
An Adaptive Reasoning Approach Towards Efficient Ordering of Composite Hypotheses
, 1991
"... u! A Bayesian network is a knowledge representation framework for encoding both qualitative and quantitative probabilistic dependencies among a set of propositional (or random) variables. An important type of probabilistic inference in a Bayesian network is the derivation of the most probable compos ..."
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Cited by 2 (2 self)
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u! A Bayesian network is a knowledge representation framework for encoding both qualitative and quantitative probabilistic dependencies among a set of propositional (or random) variables. An important type of probabilistic inference in a Bayesian network is the derivation of the most probable composite hypotheses  a setof hypotheses composed of multiple variables in a network. Such a type of probabilistic inference, however, is computationally intractable. In this paper an adaptive reasoning approach based on qualitative interval arithmetic is proposed as a method of dealing with the computational problem. Using this approach, a qualitative boundary, which reflects the upper and lower limits of a posterior likelihood, can be derived for each composite hypothesis. The advantage of bounding each composite hypothesis qualitatively is that the quantitative values of the posterior likelihoods are not all necessary in the course of an inference. Consequently, an exhaustive evaluation can ...
Using Dynamic Bayesian Networks for a Decision Support System Application to the Monitoring of Patients Treated by Hemodialysis
 in &quot;1st International Computer Systems & Information Technology Conference  ICSIT’05 1st, Alger, Algérie&quot;, IEEE
, 2005
"... A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. Dynamic Bayesian networks are an extension of Bayesian networks for modeling dynamic processes. In this paper we present a decision support system based on a dynamic Bayesian network. Its pu ..."
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Cited by 2 (0 self)
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A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. Dynamic Bayesian networks are an extension of Bayesian networks for modeling dynamic processes. In this paper we present a decision support system based on a dynamic Bayesian network. Its purpose is to monitor the dry weight of patients suffering from chronic renal failure treated by hemodialysis. 1.
Structure inference of Bayesian networks from data: A new approach based on generalized conditional entropy
 in ‘EGC
, 2008
"... Abstract. We propose a novel algorithm for extracting the structure of a Bayesian network from a dataset. Our approach is based on generalized conditional entropies, a parametric family of entropies that extends the usual Shannon conditional entropy. Our results indicate that with an appropriate c ..."
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Cited by 1 (1 self)
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Abstract. We propose a novel algorithm for extracting the structure of a Bayesian network from a dataset. Our approach is based on generalized conditional entropies, a parametric family of entropies that extends the usual Shannon conditional entropy. Our results indicate that with an appropriate choice of a generalized conditional entropy we obtain Bayesian networks that have superior scores compared to similar structures obtained by classical inference methods. 1
Edge Evaluation in Bayesian Network Structures
"... We propose a measure for assessing the degree of influence of a set of edges of a Bayesian network on the overall fitness of the network, starting with probability distributions extracted from a data set. Standard fitness measures such as the CooperHerskowitz score or the score based on the minimum ..."
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We propose a measure for assessing the degree of influence of a set of edges of a Bayesian network on the overall fitness of the network, starting with probability distributions extracted from a data set. Standard fitness measures such as the CooperHerskowitz score or the score based on the minimum description length are computationally expensive and do not focus on local modifications of networks. Our approach can be used for simplifying the Bayesian network structures without significant loss of fitness. Experimental work confirms the validity of our approach. Keywords: Bayesian belief network, KullbachLeibler divergence, entropy, edge pruning 1
Generation Of Bayesian Networks From Databases
"... Current applications of Bayesian belief networks rely on a laborious and time consuming process to elicit knowledge from human experts. The objective of this paper is to study automatic construction of Bayesian belief networks from databases. Previously, researchers have only focused on obtaining ne ..."
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Current applications of Bayesian belief networks rely on a laborious and time consuming process to elicit knowledge from human experts. The objective of this paper is to study automatic construction of Bayesian belief networks from databases. Previously, researchers have only focused on obtaining networks which best approximate the databases, and on the cases that the databases for network reconstruction are generated from models with polytree network topologies. We have developed an algorithm which guarantees the network to be generated from a database is one of the optimal solutions. That is, if there exists at least one network representation for the database, the network being generated will contain no more, and no less, probabilistic (in)dependency information as compared to the database. Otherwise, the best approximated network will be generated; where the goodness of an approximation is measured in terms of the difference of the information content carried by the network and the...