Centre for Computational Neuroscience and Robotics, School of Informatics, University of Sussex, Brighton BN1 9QJ, United Kingdom.
Phys Rev Lett. 2009 Dec 4;103(23):238701. doi: 10.1103/PhysRevLett.103.238701.
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.
格兰杰因果关系是一种基于向量自回归的预测的统计因果影响概念。最初在计量经济学领域发展起来，此后在更广泛的领域得到了应用，特别是在神经科学领域。最近，转移熵，一种联合依赖过程之间时间导向信息传递的信息论度量，在同样广泛的领域中得到了应用。虽然已经认识到这两个概念必须相关，但到目前为止，它们之间的关系还没有被正式描述。在这里，我们证明对于高斯变量，格兰杰因果关系和转移熵是完全等价的，从而将自回归和信息论方法联系起来，用于数据驱动的因果推断。
