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Research on Learning of Bayesian Networks and Its Application

Author: GuoYanJun
Tutor: YeYing
School: Huazhong University of Science and Technology
Course: Probability Theory and Mathematical Statistics
Keywords: Bayesian networks principal component analysis parameter learning structure learning finance warning
CLC: O212.8
Type: Master's thesis
Year: 2009
Downloads: 119
Quote: 2
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Abstract


There are many uncertain problems in the real world and some scientific fields. As the combination of probability and graph theory, Bayesian networks can use graph theory to picture the structure of the model on one hand. On the other hand, it can make the best of the structure of the model to reduce the complexity of the problem under probability rules. So a natural and clear method is developed to deal with uncertain problems. Bayesian networks are widely used in industry, agriculture, medical treatment and national defense, etc, and it has already brought remarkable benefit both in economic and society for us. So it is of great academic meaning and utility value to have a further study of Bayesian networks.The main work and innovations of this paper are as follows:First, the overview of the Bayesian networks. The thesis introduces the background, actuality and application fields, it also summarizes the characteristics of kinds of classification models. After that, the advantages of networks are discussed compared with other methods.Second, the paper introduces some kinds of learning algorithm about Bayesian networks. In the learning of networks’parameter, principal component analysis (PCA) and the idea of constructing networks by experts are used to develop a method, which constructs the networks fully by expert’s knowledge. The method first to get all the parameters from domain experts by a“probability scale”, after determining each expert’s weight by some index, we can get the accurate value by average weight. In the process, PCA is used to deal with the score of each expert, which eliminates the dependence between variables. The method is useful both in declining the influence of subjective factors and improving the result. In the learning of network’s structure, a statistic estimator called likelihood-ratio sample-testing is used to construct Bayesian networks. The main idea of this method is to examining the independence between every two variables through the estimator.At last, finance warning is important for enterprise. In this paper, we first use the PCA to deal with twelve economic indexes, and then we construct a na?ve Bayes model to make the finance warning. The experimental result indicates that the model can even achieve the same level with Logistic regression technique, and it also has the advantages of Bayesian networks. So it is of great value for finance analysts to study it.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > Bayesian statistics
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