基于Copula的多变量运动想象脑电信号因果分析方法

Multivariate Causality Analysis Method of Motor Imagery EEG Signals Based on Copula

目的研究一种基于Copula模型的多变量因果关系分析方法,克服格兰杰因果(Granger causality,GC)方法受限于检测线性因果关系的缺点。方法首先通过时间序列历史信息计算多个变量的联合分布函数,其次计算基于核函数估计方法的边缘条件分布,并结合秩统计方法估计经验条件Copula密度函数,然后应用Bernstein逼近法估计出最优的Copula密度函数,最后在最优估计基础上采用对数似然比构造了面向多元协变量的条件Copula-Granger因果关系。结果与线性GC、方差GC、核GC等方法相比,该方法在识别具有非线性、高阶的真实因果关系时具有较好的准确率和较低的误检率。结论本文方法能够定量地刻画运动想象任务中3个脑区(C3,Cz,C4)之间的相互影响,为效应性脑连接提供一种有效的因果测度。

Objective To overcome the limitation of detecting linear causality with the Granger causality（ GC）approach,a multivariate causality analysis algorithm was proposed based on copula model. Methods First,the joint distribution function of multiple variables was calculated by the historical information of time series. Second,the edge condition distribution was calculated based on kernel function estimation algorithm,and the empirical condition copula density function was estimated by the rank statistical approach. Then the Bernstein approximation method was used to estimate the optimal copula. Finally,the conditional copula-Granger causality for multivariate covariates was constructed in terms of the log-likelihood ratio. Results Compared with linear GC,variance GC and kernel GC algorithms,the proposed method could detect the real cause-effect relationship in nonlinear and high-order causality with better accuracy and lower false positive ratio. Conclusion The proposed method can quantitatively reveal the causal interactions among three brain regions（ C3,Cz and C4）in motor imagery tasks,and offer a good causality measure on effective brain connectivity.