小数据集下基于改进QMAP算法的BN参数学习  

BN parameter learning based on improved QMAP algorithm under small data set conditions

作　　者：陈海洋[1] 张静 王露楠 环晓敏 CHEN Haiyang;ZHANG Jing;WANG Lunan;HUAN Xiaomin(School of Electronics and Information,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学电子信息学院,陕西西安710048

出　　处：《西安工程大学学报》2023年第1期126-133,共8页Journal of Xi’an Polytechnic University

基　　金：国家自然科学基金(51905405)。

摘　　要：贝叶斯网络(bayesian network,BN)小数据集条件下,定性最大后验概率(qualitative maximum a posteriori,QMAP)估计往往会违反给定的专家约束,这就导致QMAP估计偏离真实值。为了克服该算法的缺陷,提出了一种改进的QMAP算法。首先,学习出QMAP估计,再结合保序回归方法对违反不等式约束的参数进行校正;然后使用一种微调策略对校正后的参数做进一步调整,使所得参数能够满足专家约束;最后,与最大似然估计(maximum likelihood estimation,MLE)和QMAP算法对比。仿真实验结果表明:在小数据集条件下,提出的算法满足所有约束条件,KL(Kullback-Leibler)散度始终低于其他2种算法,运行时间高于其他2种算法约0.1 s,影响甚微,且推理结果贴近真实值,偏差维持在±0.05之间。改进的QMAP算法的综合性能优于MLE、QMAP算法,并具有较好的实用性。Under the condition of Bayesian network(BN)small data set,the qualitative maximum a posteriori(QMAP)estimation tends to violate expert constraints,which causes the QMAP estimation to deviate the true value.In order to overcome the shortcomings of this algorithm,an improved QMAP algorithm was proposed.Firstly,the QMAP estimation was learned.Next,the parameters that violated the inequality constraints were regulated by the isotonic regression method.Then,the regulated parameters were further adjusted by using a fine-tuning strategy,in order to make the obtained parameters satisfy the expert constraints.Finally,a comparison was made with the maximum likelihood estimation(MLE)algorithm and QMAP algorithm.The simulation results show that under the condition of small data set,the proposed algorithm meets all the constraints:(1)the KL(Kullback-Leibler)divergence is always lower than the other two algorithms;(2)the running time is approximately 0.1 s more than the other two algorithms,which has little influence;and(3)the inference results are close to the real value,with the deviation maintaining between±0.05.The comprehensive performance of the improved QMAP algorithm is better than that of MLE and QMAP algorithm,and it has good practicability.

关 键 词：贝叶斯网络(BN) 参数学习 小数据集 定性最大后验概率(QMAP) 保序回归 KL散度 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]