标题： 基于成对时滞传递熵的非线性网络重构 显示英文标题

标题： Nonlinear Network Reconstruction by Pairwise Time-delayed Transfer Entropy

摘要： 分析网络结构连通性对于理解跨学科复杂网络的动力学和功能至关重要。 在许多网络中，结构连通性是不可观测的，这需要通过因果推断方法进行推断。 其中，转移熵（TE）由于其无模型特性，是最广泛应用于因果度量的方法之一。 然而，TE在高维概率估计中常常面临维度灾难的问题，而推断出的因果连通性与潜在结构连通性之间的关系仍然不明确。 在这里，我们通过提出一种成对时间延迟转移熵（PTD-TE）方法来解决这些问题。 我们理论上建立了PTD-TE值与节点耦合强度之间的二次关系，并证明了其对维度问题的免疫性和广泛的适用性。 在生物神经网络、非线性物理系统和脑电生理数据上的测试表明，PTD-TE能够实现一致且高性能的重构。 与现有的一系列网络连通性重构方法相比，PTD-TE在准确性和抗噪声能力方面在各种网络系统中都优于这些方法。 我们的框架为非线性现实世界网络的结构连通性推断提供了一个可扩展、模型无关的工具。 显示英文摘要

摘要： Analyzing network structural connectivity is crucial for understanding dynamics and functions of complex networks across disciplines. In many networks, structural connectivity is not observable, which requires to be inferred via causal inference methods. Among them, transfer entropy (TE) is one of the most broadly applied causality measure due to its model-free property. However, TE often faces the curse of dimensionality in high-dimensional probability estimation, and the relation between the inferred causal connectivity and the underlying structural connectivity remains poorly understood. Here we address these issues by proposing a pairwise time-delayed transfer entropy (PTD-TE) method. We theoretically establish a quadratic relationship between PTD-TE values and node coupling strengths, and demonstrate its immunity to dimensionality issues and broad applicability. Tests on biological neuronal networks, nonlinear physical systems, and electrophysiological data show PTD-TE achieves consistent, high-performance reconstructions. Compared to a bunch of existing approaches for network connectivity reconstruction, PTD-TE outperforms these methods across various network systems in accuracy and robustness against noise. Our framework provides a scalable, model-agnostic tool for structural connectivity inference in nonlinear real-world networks.