随机过程网络的Granger因果关系与有向信息论的联系
Relating Granger causality to directed information theory for networks of stochastic processes
摘要：
本文讨论了多个随机过程之间的信息循环的推断问题。我们讨论了两种可能的框架，在其中可以研究的问题：有向信息论和格兰杰因果关系。本文的主要目的是研究这两个框架之间的联系。在有向信息论的情况下，我们强调克莱默的因果条件反射的重要性。这种类型的条件不仅在有向信息的定义中是必要的，而且在处理因果边信息时也是必要的。我们还展示了如何有向信息分解成两个措施的总和，第一个相关的施赖伯的转移熵量化的动态方面的因果关系，而第二个，称为瞬时信息交换，量化的瞬时方面的因果关系。在回顾了格兰杰因果关系的定义之后，我们建立了它与有向信息论的联系。特别是在高斯的情况下，研究表明，Geweke的措施格兰杰因果关系对应的传递熵和瞬时信息交换。这允许提出一个信息理论的格兰杰因果关系的制定。
英文摘要：
This paper addresses the problem of inferring circulation of information between multiple stochastic processes. We discuss two possible frameworks in which the problem can be studied: directed information theory and Granger causality. The main goal of the paper is to study the connection between these two frameworks. In the case of directed information theory, we stress the importance of Kramer's causal conditioning. This type of conditioning is necessary not only in the definition of the directed information but also for handling causal side information. We also show how directed information decomposes into the sum of two measures, the first one related to Schreiber's transfer entropy quantifies the dynamical aspects of causality, whereas the second one, termed instantaneous information exchange, quantifies the instantaneous aspect of causality. After having recalled the definition of Granger causality, we establish its connection with directed information theory. The connection is particularly studied in the Gaussian case, showing that Geweke's measures of Granger causality correspond to the transfer entropy and the instantaneous information exchange. This allows to propose an information theoretic formulation of Granger causality.
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