基于D-vine Copula理论的贝叶斯分类器设计

Bayesian classifier based on D-vine Copula theory

高斯判别分析、朴素贝叶斯等传统贝叶斯分类方法在构建变量的联合概率分布时,往往会对变量间的相关性进行简化处理,从而使得贝叶斯决策理论中类条件概率密度的估计与实际数据之间存在一定的偏差.对此,结合Copula函数研究特征变量之间的相关性优化问题,设计基于D-vine Copula理论的贝叶斯分类器,主要目的是为了提高类条件概率密度估计的准确性.将变量的联合概率分布分解为一系列二元Copula函数与边缘概率密度函数的乘积,采用核函数方法对边缘概率密度进行估计,通过极大似然估计对二元Copula函数的参数分别进行优化,进而得到类条件概率密度函数的形式.将基于D-vine Copula理论的贝叶斯分类器应用到生物电信号的分类问题上,并对分类效果进行分析和验证.结果表明,所提出的方法在各项分类指标上均具备良好的性能.

In the traditional Bayesian classifiers such as the Gaussian discriminant analysis method and the Naive Bayesian method,the correlation between variables are commonly simplified when constructing the joint probability distribution of variables.Accordingly,the estimation of the class conditional probability density would have differences with the actual data.In this study,a Bayesian classifier based on the D-vine Copula theory is developed by investigating on the correlation between variables.The main objective is to improve the accuracy of the class conditional probability density estimation.The joint probability distribution of variables is decomposed into a series of pair Copula functions and marginal probability density functions.The kernel function method is adopted to estimate the marginal probability density.The parameters of pair Copula functions are optimized by the maximum likelihood estimation.The developed method is analyzed and validated on the classification of neurophysiological signals.The obtained results show that it has better performance on several classification indexes.