Research On Hierarchical Bayesian Network And Its Application

Bayesian Networks which have complete mathematic support and is based on the probabilistic and statistics theory are being used extensively for reasoning under uncertainty.But inference mechanisms for Bayesian Networks are compromised by the fact that they can only deal with propositional domains.In this work,we introduce an extension of that formalism,Hierarchical Bayesian Networks that can represent probabilistic dependencies of the domains of variables.Hierarchical Bayesian Networks are similar to Bayesian Networks,in that they represent probabilistic dependencies between variables as a directed acyclic graph,where each node of the graph corresponds to a random variable and is quantified by the conditional probability of that variable given the values of its parents in the graph.A node in Hierarchical Bayesian Networks may correspond to an aggregation of simpler types. A component of one node may itself represent a composite structure;this allows the representation of complex hierarchical domains.Furthermore,probabilistic dependencies can be expressed at any level,either between nodes that are contained in the same level or between nodes that are contained in different levels.These features make Hierarchical Bayesian Networks applicable for models with more hierarchies or more complex probabilistic dependencies and extend the expressive power of Hierarchical Bayesian Networks.The dissertation Analyzed and researched the principle and applications of Bayesian Networks.Some traditional construction, learning,inference and optimization algorithms of Bayesian Networks and Hierarchical Bayesian Networks are also introduced in the work.Besides,we applied a Na(i|¨)ve Bayesian Network and a Hierarchical Bayesain Network to handwritten Bangla digit recognition.The average recognition rate of the Na(i|¨)ve Bayesian Network reached 92.1%and the highest rate 93.47%of the composite classifier was reached after 3 iterations with optimized AdaBoost algorithm.However,the average recognition rate reduced slightly with further iterations.The average recognition rate of the Hierarchical Bayesian Network was 87.5%in trial.After experiments,we made further comparison between test results of the systems.