Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy
Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy
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DOI：
10.1103/physreve.86.061121
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发表时间：
2012-12-17
影响因子：
2.4
通讯作者：
Kurths, Juergen
中科院分区：
文献类型：
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作者：
Runge, Jakob;Heitzig, Jobst;Kurths, Juergen
虽然确定多变量时间序列的两个组成部分之间存在因果关系是一个重要问题，但Runge， Heitzig， Petoukhov和Kurths[物理学家]提出了一个主题。Rev. Lett. 108, 258701(2012)]，更重要的是以一种有意义的方式评估它们的关联强度。在本文中，我们重点讨论了使用信息理论度量来定义有意义的耦合强度的问题，并展示了众所周知的互信息和传递熵的缺点。相反，我们提出了一个特定的时间延迟条件互信息，即瞬间信息传递（MIT），作为一种延迟特定的关联度量，它是一般的，因果的，反映了耦合强度的一个很好解释的概念，并且实际上是可计算的。基于信息论，麻省理工学院是通用的，因为它不假设产生时间序列的过程背后有特定的模型类。正如之前的一篇论文[Runge， Heitzig, Petoukhov, and Kurths， Phys]中所讨论的那样。Rev. Lett. 108, 258701(2012)]，图形模型的一般框架使MIT具有因果性，因为它仅对剩余过程中不独立的滞后组件给出非零值。此外，图形模型允许条件的低维表述，这对于条件互信息的可靠估计很重要，因此使得MIT实际上是可计算的。MIT基于源熵的基本概念，我们利用它来产生耦合强度的概念，即与互信息和传递熵相比，耦合强度的概念很好地解释了，在许多情况下，它仅取决于两个组件在一定滞后时的相互作用。因此，MIT在许多情况下能够以信息理论的方式排除进程中自依赖性的误导性影响。我们对一类一般的非线性随机过程形式化并用分析和数值方法证明了这一想法，并说明了MIT在气候数据上的潜力。DOI: 10.1103 / PhysRevE.86.061121
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge, Heitzig, Petoukhov, and Kurths [Phys. Rev. Lett. 108, 258701 (2012)], it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of defining a meaningful coupling strength using information-theoretic measures and demonstrate the shortcomings of the well-known mutual information and transfer entropy. Instead, we propose a certain time-delayed conditional mutual information, the momentary information transfer (MIT), as a lag-specific measure of association that is general, causal, reflects a well interpretable notion of coupling strength, and is practically computable. Rooted in information theory, MIT is general in that it does not assume a certain model class underlying the process that generates the time series. As discussed in a previous paper [Runge, Heitzig, Petoukhov, and Kurths, Phys. Rev. Lett. 108, 258701 (2012)], the general framework of graphical models makes MIT causal in that it gives a nonzero value only to lagged components that are not independent conditional on the remaining process. Further, graphical models admit a low-dimensional formulation of conditions, which is important for a reliable estimation of conditional mutual information and, thus, makes MIT practically computable. MIT is based on the fundamental concept of source entropy, which we utilize to yield a notion of coupling strength that is, compared to mutual information and transfer entropy, well interpretable in that, for many cases, it solely depends on the interaction of the two components at a certain lag. In particular, MIT is, thus, in many cases able to exclude the misleading influence of autodependency within a process in an information-theoretic way. We formalize and prove this idea analytically and numerically for a general class of nonlinear stochastic processes and illustrate the potential of MIT on climatological data. DOI: 10.1103/PhysRevE.86.061121