影响图模型选择中存在数据依赖性、计算复杂性和非概率关系问题.通过对影响图结构进行分解,提出PS-EM 算法对影响图的概率结构部分进行模型选择.给出一种 BP 神经网络,通过对局部效用函数的学习实现效用结构部分的模型选择,并引入权重...影响图模型选择中存在数据依赖性、计算复杂性和非概率关系问题.通过对影响图结构进行分解,提出PS-EM 算法对影响图的概率结构部分进行模型选择.给出一种 BP 神经网络,通过对局部效用函数的学习实现效用结构部分的模型选择,并引入权重阈值来避免过拟合.PS-EM 算法是在 SEM 算法中引入一种融合先验知识的MDL 评分标准来降低传统 MDL 评分对数据的依赖性,并通过将参数学习和结构评分分开计算提高计算效率.算法比较的结果显示 PS-EM 比标准 SEM 的时间性能好、对数据依赖性小,且效用部分的结构选择易于实现.展开更多
Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and exp...Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.展开更多
文摘影响图模型选择中存在数据依赖性、计算复杂性和非概率关系问题.通过对影响图结构进行分解,提出PS-EM 算法对影响图的概率结构部分进行模型选择.给出一种 BP 神经网络,通过对局部效用函数的学习实现效用结构部分的模型选择,并引入权重阈值来避免过拟合.PS-EM 算法是在 SEM 算法中引入一种融合先验知识的MDL 评分标准来降低传统 MDL 评分对数据的依赖性,并通过将参数学习和结构评分分开计算提高计算效率.算法比较的结果显示 PS-EM 比标准 SEM 的时间性能好、对数据依赖性小,且效用部分的结构选择易于实现.
基金supported by the National Natural Science Foundation of China under Grant No.11165016
文摘Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.
