Structure Learning Algorithm Of Bayesian Network Based On Small Samples And It’s Application

The Bayesian Network (BN) is a directed acyclic graph(DAG) which isblending with a probability distribution table(CPT). It combines the sampleinformation with prior knowledge and describes the dependent relationshipbetween qualitative variables and quantitative variables in a form of directededge and CPT respectively.So BN not only have the characteristics of imageintuitive data expression,but also own solid theory foundation and reasoningability. As a result, BN is an effective tool for modeling and reasoning,andhas a wide range of applications,for instance,in data mining,classificationreasoning,medical diagnosis and engineering decisions and so on.Learning the structure is the basis of solving practical problems and ahotspot for BN theory research which contains two parts.One is ensuring itsstructure(DAG),the other is learning conditional probability distribution ofnode variables(CPT). Among them,structure learning is the foundation of allthe learning works. Recently, there are lots of classic and practical algorithmsin the structure learning areas,such as hill-climbing algorithm. All thosealgorithms, however, are based on a large dataset.But many experiments cannot be repeated in practical problems resulting in less experiments data andsmall size. Thus,incomplete information in such a small sample dataset willnot guarantee the accuracy and reliability of the BN structure learning. Inview of this,we develop the research on the BN structure learning on the basisof small sample dataset.we do such works below:For the small sample sets in practical problems,we introduced theprobability density kernel estimation method to achieve the expansion of theoriginal sample set,and then using the K2algorithm for a Bayesian networkstructure learning. By optimizing the kernel function and window width,weachieved the effective expansion of the original sample sets based onprobability density kernel estimation.Meanwhile,based on mutualinformation,we confirmed the variable order and established a Bayesianstructure learning algorithm named KI-K2on a small sample sets. Simulationresults show that the KI-K2algorithm is effective and practical.This paper introduces a variety of reasoning analysis model which BNcan apply for performance estimate and decision analysis.Then based on actual project fact,it sets up a helicopter simulation model with four controlchannels,and a confirmation application in a example of unmanned helicopteris carried out. Follow on, small simple data sets for testing are obtained afterseveral helicopter simulation model experiments.Based on these small simpledata and KI-K2structure learning algorithm mentioned in this paper, we willresearch structure learning and parameter learning.Finally, on the basis ofparameter performance and operational decision of BN to helicopter,we makeinference which will strongly guide for training and practice.