Abstract

Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms of microscopic configurations rely on some approximation of independence among dynamical variables, thus introducing a systematic bias in the prediction of the ground-truth dynamics. Here, we develop a combinatorial framework based on the approximation that spreading may occur only along the shortest paths connecting pairs of nodes. The approximation overestimates dynamical correlations among node states and leads to biased predictions. Systematic bias is, however, pointing in the opposite direction of existing approximations. We show that the combination of the two biased approaches generates predictions of the ground-truth dynamics that are more accurate than the ones given by the two approximations if used in isolation. We further take advantage of the combinatorial approximation to characterize theoretical properties of some inference problems, and show that the reconstruction of microscopic configurations is very sensitive to both the place where and the time when partial knowledge of the system is acquired.

Graphic Abstract

中文翻译：

---

组合方法在网络上扩展流程

摘要

在复杂的网络拓扑上定义的随机传播模型用于模拟现实系统中疾病，信息和观点的传播。现有的以微观形态表征模型的理论方法依赖于动力学变量之间独立性的某种近似，因此在地面真相动力学的预测中引入了系统性偏差。在这里，我们基于这样的近似值开发了一个组合框架：扩展可能仅沿着连接节点对的最短路径发生。近似值高估了节点状态之间的动态相关性，并导致预测有偏差。但是，系统偏差指向与现有近似值相反的方向。我们表明，两种偏倚方法的组合生成的地面真实动态预测比单独使用两个近似值所给出的预测更准确。我们进一步利用组合近似来刻画一些推理问题的理论性质，并表明微观构型的重构对获取系统部分知识的地点和时间都非常敏感。

图形摘要