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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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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.
Searching for Bayesian Network Structures in the Space of Restricted Acyclic Aprtially Directed Graphs
 Journal of Artificial Intelligence Research
, 2003
"... Although many algorithms have been designed to construct Bayesian network structures using dierent approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function and a search procedure (although some methods combine the two). ..."
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Cited by 21 (2 self)
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Although many algorithms have been designed to construct Bayesian network structures using dierent approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function and a search procedure (although some methods combine the two). Within the score+search paradigm, the dominant approach uses local search methods in the space of directed acyclic graphs (DAGs), where the usual choices for de ning the elementary modi cations (local changes) that can be applied are arc addition, arc deletion, and arc reversal. In this paper, we propose a new local search method that uses a dierent search space, and which takes account of the concept of equivalence between network structures: restricted acyclic partially directed graphs (RPDAGs). In this way, the number of dierent con gurations of the search space is reduced, thus improving eciency. Moreover, although the nal result must necessarily be a local optimum given the nature of the search method, the topology of the new search space, which avoids making early decisions about the directions of the arcs, may help to nd better local optima than those obtained by searching in the DAG space.
An efficient data mining method for learning Bayesian networks using an evolutionary algorithmbased hybrid approach
, 2004
"... Abstract—Given the explosive growth of data collected from current business environment, data mining can potentially discover new knowledge to improve managerial decision making. This paper proposes a novel data mining approach that employs an evolutionary algorithm to discover knowledge represented ..."
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Abstract—Given the explosive growth of data collected from current business environment, data mining can potentially discover new knowledge to improve managerial decision making. This paper proposes a novel data mining approach that employs an evolutionary algorithm to discover knowledge represented in Bayesian networks. The approach is applied successfully to handle the business problem of finding response models from direct marketing data. Learning Bayesian networks from data is a difficult problem. There are two different approaches to the network learning problem. The first one uses dependency analysis, while the second one searches good network structures according to a metric. Unfortunately, both approaches have their own drawbacks. Thus, we propose a novel hybrid algorithm of the two approaches, which consists of two phases, namely, the conditional independence (CI) test and the search phases. In the CI test phase, dependency analysis is conducted to reduce the size of the search space. In the search phase, good Bayesian network models are generated by using an evolutionary algorithm. A new operator is introduced to further enhance the search effectiveness and efficiency. In a number of experiments and comparisons, the hybrid algorithm outperforms MDLEP, our previous algorithm which uses evolutionary programming (EP) for network learning, and other network learning algorithms. We then apply the approach to two data sets of direct marketing and compare the performance of the evolved Bayesian networks obtained by the new algorithm with those by MDLEP, the logistic regression models, the naïve Bayesian classifiers, and the treeaugmented naïve Bayesian network classifiers (TAN). In the comparison, the new algorithm outperforms the others. Index Terms—Bayesian networks, data mining, evolutionary computation, evolutionary programming (EP). I.
Evolving Dynamic Bayesian Networks with Multiobjective Genetic Algorithms
, 2005
"... A dynamic Bayesian network (DBN) is a probabilistic network that models interdependent entities that change over time. Given example sequences of multivariate data, we use a genetic algorithm to synthesize a network structure that models the causal relationships that explain the sequence. We use a m ..."
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A dynamic Bayesian network (DBN) is a probabilistic network that models interdependent entities that change over time. Given example sequences of multivariate data, we use a genetic algorithm to synthesize a network structure that models the causal relationships that explain the sequence. We use a multiobjective evaluation strategy with a genetic algorithm. The multiobjective criteria are a network’s probabilistic score and structural complexity score. Our use of Pareto ranking is ideal for this application, because it naturally balances the effect of the likelihood and structural simplicity terms used in the BIC network evaluation heuristic. We use a simple structural scoring formula, which tries to keep the number of links in the network approximately equivalent to the number of variables. We also use a simple representation that favours sparsely connected networks similar in structure to those modeling biological phenomenon. Our experiments show promising results when evolving networks ranging from 10 to 30 variables, using a maximal connectivity of between 3 and 4 parents per node. The results from the multiobjective GA were superior to those obtained with a single objective GA.
Stochastic Local Algorithms for Learning Belief Networks: Searching in the Space of the Orderings
"... Abstract. An important type of methods for learning belief networks from data are those based on the use of a scoring metric, to evaluate the fitness of any given candidate network to the data base, and a search procedure to explore the set of candidate networks. In this paper we propose a new metho ..."
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Abstract. An important type of methods for learning belief networks from data are those based on the use of a scoring metric, to evaluate the fitness of any given candidate network to the data base, and a search procedure to explore the set of candidate networks. In this paper we propose a new method that carries out the search not in the space of directed acyclic graphs but in the space of the orderings of the variables that compose the graphs. Moreover, we use a new stochastic search method to be applied to this problem, Variable Neighborhood Search. We also experimentally compare our methods with some other search procedures commonly used in the literature.
Learning Right Sized Belief Networks by Means of a Hybrid Methodology ⋆
"... Abstract. Previous algoritms for the construction of belief networks structures from data are mainly based either on independence criteria or on scoring metrics. The aim of this paper is to present a hybrid methodology that is a combination of these two approaches, which benefits from characteristic ..."
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Abstract. Previous algoritms for the construction of belief networks structures from data are mainly based either on independence criteria or on scoring metrics. The aim of this paper is to present a hybrid methodology that is a combination of these two approaches, which benefits from characteristics of each one, and to introduce an operative algoritm based on this methodology. We dedicate a special attention to the problem of getting the ‘right ’ size of the belief network induced from data, i.e. finding a tradeoff between network complexity and accuracy. We propose several approaches to tackle this matter. Results of the evaluation of the algorithm on the wellknown Alarm network are also presented. 1
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"... In knowledge discovery from databases, we emphasize the need for learning from huge, incomplete and imperfect data sets (PiatetskyShapiro and Frawley, 1991). To handle noise in the problem domain, existing learning systems avoid overfitting the imperfect training examples by excluding insignificant ..."
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In knowledge discovery from databases, we emphasize the need for learning from huge, incomplete and imperfect data sets (PiatetskyShapiro and Frawley, 1991). To handle noise in the problem domain, existing learning systems avoid overfitting the imperfect training examples by excluding insignificant patterns. The problem is that these systems use a limiting attributevalue language for representing the training examples and induced knowledge. Moreover, some important patterns are ignored because they are statistically insignificant. This paper describes a system called GLPS that combines Genetic Algorithms and a variation of FOIL (Quinlan, 1990) to learn firstorder concepts from noisy training examples. The performance of GLPS is evaluated on the chess endgame domain. A detail comparison to FOIL is accomplished and the performance of GLPS is significantly better than that of FOIL. This result indicates that the Darwinian principle of natural selection is a plausible noise handling method which can avoid overfitting and identify important patterns at the same time. 1.
Partial abductive inference in Bayesian belief networks by simulated annealing Luis M. de Campos a, Jose A.Gamez b, * , Serafõn Moral a
, 2000
"... ..."
Abstract A hybrid methodology for learning belief networks: BENEDICT
, 2000
"... Previous algorithms for the construction of belief networks structures from data are mainly based either on independence criteria or on scoring metrics. The aim of this paper is to present a hybrid methodology that is a combination of these two approaches, which bene®ts from characteristics of each ..."
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Previous algorithms for the construction of belief networks structures from data are mainly based either on independence criteria or on scoring metrics. The aim of this paper is to present a hybrid methodology that is a combination of these two approaches, which bene®ts from characteristics of each one, and to develop two operative algorithms based on this methodology. Results of the evaluation of the algorithms on the wellknown Alarm network are presented, as well as the algorithms performance issues and