A measure to estimate the direct and directional coupling in multivariate
time series is proposed. The measure is an extension of a recently published
measure of conditional Mutual Information from Mixed Embedding (MIME) for
bivariate time series. In the proposed measure of Partial MIME (PMIME), the
embedding is on all observed variables, and it is optimized in explaining the
response variable. It is shown that PMIME detects correctly direct coupling,
and outperforms the (linear) conditional Granger causality and the partial
transfer entropy. We demonstrate that PMIME does not rely on significance test
and embedding parameters, and the number of observed variables has no effect on
its statistical accuracy, it may only slow the computations. The importance of
these points is shown in simulations and in an application to epileptic
multi-channel scalp EEG.

提出了一种评估多变量时间序列中直接和定向耦合的方法，其扩展了最近发表的一种针对双变量时间序列的条件混合嵌入互信息（MIME）的度量。在所提出的部分 MIME（PMIME）度量中，嵌入是在所有观测变量上进行的，并且优化以解释响应变量。 展示了 PMIME 正确检测直接耦合，并优于（线性）条件 Granger 因果性和部分传输熵。 示范了 PMIME 不依赖显着性测试和嵌入参数，观察变量的数量对其统计精度没有影响，但可能会减慢计算过程。这些要点的重要性在模拟和应用于癫痫多通道头皮 EEG 中得到证明。