Identifying Influential and Vulnerable Nodes in Interaction Networks through Estimation of Transfer Entropy Between Univariate and Multivariate Time Series

Julian Lee
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Abstract

Transfer entropy (TE) is a powerful tool for measuring causal relationships within interaction networks. Traditionally, TE and its conditional variants are applied pairwise between dynamic variables to infer these causal relationships. However, identifying the most influential or vulnerable node in a system requires measuring the causal influence of each component on the entire system and vice versa. In this paper, I propose using outgoing and incoming transfer entropy-where outgoing TE quantifies the influence of a node on the rest of the system, and incoming TE measures the influence of the rest of the system on the node. The node with the highest outgoing TE is identified as the most influential, or "hub", while the node with the highest incoming TE is the most vulnerable, or "anti-hub". Since these measures involve transfer entropy between univariate and multivariate time series, naive estimation methods can result in significant errors, particularly when the number of variables is comparable to or exceeds the number of samples. To address this, I introduce a novel estimation scheme that computes outgoing and incoming TE only between significantly interacting partners. The feasibility of this approach is demonstrated by using synthetic data, and by applying it to a real data of oral microbiota. The method successfully identifies the bacterial species known to be key players in the bacterial community, demonstrating the power of the new method.
通过估算单变量和多变量时间序列之间的转移熵识别交互网络中的影响节点和脆弱节点
传递熵(TE)是测量交互网络中因果关系的有力工具。传统上,TE 及其条件变体在动态变量之间成对应用,以推断这些因果关系。然而,要识别系统中最具影响力或最脆弱的节点,就必须测量每个组件对整个系统的因果影响,反之亦然。在本文中,我建议使用传出和传入转移熵,其中传出转移熵量化节点对系统其他部分的影响,传入转移熵衡量系统其他部分对节点的影响。传出熵最高的节点被认定为最有影响力的节点,或称 "枢纽",而传入熵最高的节点则是最脆弱的节点,或称 "反枢纽"。由于这些测量方法涉及单变量和多变量时间序列之间的转移熵,因此天真的估计方法可能会导致重大误差,尤其是当变量数量与样本数量相当或超过样本数量时。为了解决这个问题,我引入了一种新的估算方法,即只计算显著相互作用伙伴之间的传出和传入 TE。通过使用合成数据以及将其应用于口腔微生物群的真实数据,证明了这种方法的可行性。该方法成功地识别了细菌群落中已知的关键细菌物种,展示了新方法的威力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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