小数据集BN建模方法及其在威胁评估中的应用

The Modeling Method with Bayesian Networks and Its Application in the Threat Assessment Under Small Data Sets

贝叶斯网络是数据挖掘领域的主要工具之一.在某些特定场合,如重大装备的故障诊断、地质灾害预测及作战决策等,希望用少量数据得到较好的结果.因此,本文针对小数据集条件下的贝叶斯网络学习问题展开研究.首先,建立基于连接概率分布的结构约束模型,提出I-BD-BPSO(Improved-Bayesian Dirichlet-Binary Particle Swarm Optimization)结构学习算法;其次,建立单调性参数约束模型,提出MCE(Monotonicity Constraint Estimation)参数学习算法;最后,应用所提算法构建威胁评估模型并应用变量消元法进行推理计算.实验结果表明,在小数据集条件下,本文的结构学习算法优于经典的二值粒子群优化算法,参数学习算法优于最大似然估计、保序回归及凸优化算法,并能够构建有效的威胁评估模型.

Bayesian network is one of the main tools for data mining.In such cases as large equipment fault diagno-sis,geological disaster forecast,operational decision,etc,good results are expected to achieve based on small data sets. Therefore,this article focuses on the problem of learning Bayesian network from small data sets.Firstly,the structure con-straint model based on the probability distribution of the connection was built.Then,the improved-Bayesian Dirichlet-binary particle swarm optimization algorithm was proposed.Secondly,the monotonicity parameter constraint model was defined and the monotonicity constraint estimation algorithm was proposed.Finally,the proposed algorithm was applied to construct the threat assessment model.Then,the model was used for reasoning with the variable elimination method.Experimental results reveal that the structure learning algorithm outperforms classical binary particle swarm optimization algorithm and the param-eter learning method surpasses maximum likelihood estimation,isotonic regression and convex optimization method for small data sets.The threat assessment model is also proved to be effective.