冗余变量与Granger因果关系
Redundant variables and Granger causality
摘要：
我们讨论了使用多变量格兰杰因果关系存在冗余变量：标准分析的应用，在这种情况下，导致低估的因果关系。使用非规范化版本的因果关系指数，我们定量地发展的概念冗余和协同作用的因果关系的框架，并提出了两种方法来分组冗余变量：（i）对于一个给定的目标，剩余的变量进行分组，以最大限度地提高总的因果关系和（ii）整个变量集进行分区，以最大限度地提高子集之间的因果关系的总和。我们展示了一个真正的神经实验的应用程序，旨在更深入地了解偏头痛大脑中异常神经元振荡的生理基础。我们的方法的结果揭示了由于重复的经颅磁刺激引起的信息模式的变化。
英文摘要：
We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under-estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables: (i) for a given target, the remaining variables are grouped so as to maximize the total causality and (ii) the whole set of variables is partitioned to maximize the sum of the causalities between subsets. We show the application to a real neurological experiment, aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain. The outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations.
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