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Research on Bayesian Network

Author: HuangYouPing
Tutor: ShiZhongZhi
School: Institute of Computing Technology
Course: Computer Software and Theory
Keywords: Bayesian Network Conditional Independence Naive Bayesian Classification Dynamic Bayesian Network Information Geometry Statistic Manifold Riemman measure Fisher Information Matrix Fisher Score Information Retrieving Rules Based Method Text Classification Subject Words Tree Hierarchical Classification
CLC: TP18
Type: PhD thesis
Year: 2005
Downloads: 2424
Quote: 32
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Abstract


Bayesian network(BN) is one of the most important methods of dealing with uncertainty problems. It has complete mathematic support and is based on the probabilistic and statistics theory. Because of its natural knowledge representation, powerful reasoning ability, as well as convenient decision-making mechanism, it is applied in many domains now. After introducing the theory framework of Bayesian network, this paper carried out the following research: researching Bayesian network based on information geometry theory, improving the performance of naive Bayesian classification(NBC), retrieving information from semi-structured text using rules embedded dynamic Bayesian network, and hierarchical text classification model based on Bayesian network. The contributions of this dissertation are as follows:(1) Analyzing the characteristics of the statistic manifold corresponded to the special probabilistic distribution family-Bayesian network. BN’s conditional independence will reduce the dimension of the manifold, and simplify the Riemman measure matrix. Putting forward an algorithm for learning BN’s parameters from incomplete data based on information geometry: natural gradient on Bayesian network. Deducing the natural gradient calculation formula for discrete BN , continuous BN, conditional Gaussian network and BN with discrete children of continuous parents. Demonstrating that natural gradient is more reasonable and more fast than Euclidean gradient by theory and by experiment.(2) Putting forward a new method to improve the performance of NBC by by creating new attributes from the original attributes, then improving the conditional independence of attributes: Constructing NBC based on Fisher score. The new attributes are the partial differential on the distribution parameters of the log -distribution function. We prove that the new attributes obtained by Fisher score map are condition independent on each other under certain conditions. Then we analyzed the condition independence of new attributes for two special distributions: discrete distribution without any prior information and the distribution in which the attributes are condition independent already. The experiment results shows that this method has excellent performance.(3) Putting forward a new algorithm of text information retrieving: rules

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