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Learning the naive Bayes classifier with optimization models

100%
Taheri S., Mammadov M.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 4
787-795
EN
Naive Bayes is among the simplest probabilistic classifiers. It often performs surprisingly well in many real world applications, despite the strong assumption that all features are conditionally independent given the class. In the learning process of this classifier with the known structure, class probabilities and conditional probabilities are calculated using training data, and then values of these probabilities are used to classify new observations. In this paper, we introduce three novel optimization models for the naive Bayes classifier where both class probabilities and conditional probabilities are considered as variables. The values of these variables are found by solving the corresponding optimization problems. Numerical experiments are conducted on several real world binary classification data sets, where continuous features are discretized by applying three different methods. The performances of these models are compared with the naive Bayes classifier, tree augmented naive Bayes, the SVM, C4.5 and the nearest neighbor classifier. The obtained results demonstrate that the proposed models can significantly improve the performance of the naive Bayes classifier, yet at the same time maintain its simple structure.
2
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Node assignment problem in Bayesian networks

100%
Polanska J., Borys D., Polanski A.
International Journal of Applied Mathematics and Computer Science
|
2006
|
tom 16
|
nr 2
233-240
EN
This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.
3
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Bayesian reliability models of Weibull systems: State of the art

88%
Zaidi A., Ould Bouamama B., Tagina M.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 3
585-600
EN
In the reliability modeling field, we sometimes encounter systems with uncertain structures, and the use of fault trees and reliability diagrams is not possible. To overcome this problem, Bayesian approaches offer a considerable efficiency in this context. This paper introduces recent contributions in the field of reliability modeling with the Bayesian network approach. Bayesian reliability models are applied to systems with Weibull distribution of failure. To achieve the formulation of the reliability model, Bayesian estimation of Weibull parameters and the model's goodness-of-fit are evoked. The advantages of this modelling approach are presented in the case of systems with an unknown reliability structure, those with a common cause of failures and redundant ones. Finally, we raise the issue of the use of BNs in the fault diagnosis area.
4
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Evolutionary computation based on Bayesian classifiers

75%
Miquélez T., Bengoetxea E., Larrañaga P.
International Journal of Applied Mathematics and Computer Science
|
2004
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tom 14
|
nr 3
335-349
EN
Evolutionary computation is a discipline that has been emerging for at least 40 or 50 years. All methods within this discipline are characterized by maintaining a set of possible solutions (individuals) to make them successively evolve to fitter solutions generation after generation. Examples of evolutionary computation paradigms are the broadly known Genetic Algorithms (GAs) and Estimation of Distribution Algorithms (EDAs). This paper contributes to the further development of this discipline by introducing a new evolutionary computation method based on the learning and later simulation of a Bayesian classifier in every generation. In the method we propose, at each iteration the selected group of individuals of the population is divided into different classes depending on their respective fitness value. Afterwards, a Bayesian classifier-either naive Bayes, seminaive Bayes, tree augmented naive Bayes or a similar one-is learned to model the corresponding supervised classification problem. The simulation of the latter Bayesian classifier provides individuals that form the next generation. Experimental results are presented to compare the performance of this new method with different types of EDAs and GAs. The problems chosen for this purpose are combinatorial optimization problems which are commonly used in the literature.
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