网络传递熵和度量空间在因果关系推断中的应用
Network Transfer Entropy and Metric Space for Causality Inference
摘要：
一个措施来量化的加权网络中的顶点对之间的有向信息传输，在指定的最大长度的路径。我们的方法采用了一个通用的，网络流量的概率模型，从两个加权网络动态之间的信息距离可以自然地表示为詹森香农分歧（JSD）。我们的网络传输熵的措施是能够区分和量化网络元素之间的因果关系，在简单的合成网络和生物信号网络的应用。最后，我们的框架的理论扩展，其中的平方根的JSD诱导加权网络上的动态空间的度量。我们证明了一个收敛准则，证明了一种形式的收敛在一个家庭的矩阵度量空间中的加权网络的结构意味着他们的动态收敛的平方根JSD度量。
英文摘要：
A measure is derived to quantify directed information transfer between pairs of vertices in a weighted network, over paths of a specified maximal length. Our approach employs a general, probabilistic model of network traffic, from which the informational distance between dynamics on two weighted networks can be naturally expressed as a Jensen Shannon Divergence (JSD). Our network transfer entropy measure is shown to be able to distinguish and quantify causal relationships between network elements, in applications to simple synthetic networks and a biological signalling network. We conclude with a theoretical extension of our framework, in which the square root of the JSD induces a metric on the space of dynamics on weighted networks. We prove a convergence criterion, demonstrating that a form of convergence in the structure of weighted networks in a family of matrix metric spaces implies convergence of their dynamics with respect to the square root JSD metric.
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