一种基于结构分解和因子分析的贝叶斯网络隐变量发现算法

摘要

Hidden variables are unobservable or virtual variables, and the hidden variables cannot be effectively discovered by directly using the learning methods of data driven. The structure analysis methods are used to find hidden variables. Bcause the number and location of hidden variables are difficult to be determined,a learning algorithm(S-FAHF) of hidden variables was presented based on structural decomposition and factor analysis. The S-FAHF algorithm obtains the variables sets(Cliques) by junction tree algorithm, and the variables in a set have stronger dependence relationships. Then,the factor analysis method is inducted to discriminate the number and location of hidden variables for cliques;finally, the BIC scoring function is used to test validity of hidden variables. The results of algorithm comparison and experiment show that S-FAHF algorithm can effectively determine the number of hidden variables and their location.%隐变量是观察不到或虚拟的变量,直接利用数据驱动的学习方法难以有效地发现隐变量,因而需要结合概率图结构分析的方法.针对基于结构分析的隐变量发现方法中难以确定隐变量个数和位置的问题,提出一种基于结构分解和因子分析的隐变量发现算法(S-FAHF).S-FAHF算法利用联合树算法生成具较强依赖关系的变量子集,利用因子分析思想,通过求变量子集的特征值和累积贡献率确定变量子集中隐变量的个数,利用负荷矩阵确定隐变量的位置,最后利用打分函数测试所发现的隐变量的有效性.通过算法比较和实验结果表明,该方法能准确地确定贝叶斯网络中隐变量的个数及位置.