National ICT Australia, Canberra Research Laboratory, College of Engineering and Computer Science, Australian National University, Canberra 2601, Australia.
Neural Comput. 2012 Jul;24(7):1722-39. doi: 10.1162/NECO_a_00291. Epub 2012 Mar 19.
Detecting and characterizing causal interdependencies and couplings between different activated brain areas from functional neuroimage time series measurements of their activity constitutes a significant step toward understanding the process of brain functions. In this letter, we make the simple point that all current statistics used to make inferences about directed influences in functional neuroimage time series are variants of the same underlying quantity. This includes directed transfer entropy, transinformation, Kullback-Leibler formulations, conditional mutual information, and Granger causality. Crucially, in the case of autoregressive modeling, the underlying quantity is the likelihood ratio that compares models with and without directed influences from the past when modeling the influence of one time series on another. This framework is also used to derive the relation between these measures of directed influence and the complexity or the order of directed influence. These results provide a framework for unifying the Kullback-Leibler divergence, Granger causality, and the complexity of directed influence.
从功能神经影像时间序列测量的活动中检测和描述不同激活脑区之间的因果相互依赖和耦合，是理解大脑功能过程的重要步骤。在这封信中，我们提出了一个简单的观点，即目前用于对功能神经影像时间序列中定向影响进行推断的所有统计方法都是同一基本数量的变体。这包括有向转移熵、互信息、Kullback-Leibler 公式、条件互信息和 Granger 因果关系。至关重要的是，在自回归建模的情况下，基本数量是似然比，当对一个时间序列对另一个时间序列的影响进行建模时，它比较了有和没有过去定向影响的模型。该框架还用于推导出这些定向影响度量与定向影响的复杂性或阶数之间的关系。这些结果为统一 Kullback-Leibler 散度、Granger 因果关系和定向影响的复杂性提供了一个框架。
