Gajewski Łukasz G, Chołoniewski Jan, Wilinski Mateusz
Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland.
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E. 2021 Aug;104(2-1):024309. doi: 10.1103/PhysRevE.104.024309.
When dealing with spreading processes on networks it can be of the utmost importance to test the reliability of data and identify potential unobserved spreading paths. In this paper we address these problems and propose methods for hidden layer identification and reconstruction. We also explore the interplay between difficulty of the task and the structure of the multilayer network describing the whole system where the spreading process occurs. Our methods stem from an exact expression for the likelihood of a cascade in the susceptible-infected model on an arbitrary graph. We then show that by imploring statistical properties of unimodal distributions and simple heuristics describing joint likelihood of a series of cascades one can obtain an estimate of both existence of a hidden layer and its content with success rates far exceeding those of a null model. We conduct our analyses on both synthetic and real-world networks providing evidence for the viability of the approach presented.
在处理网络上的传播过程时，测试数据的可靠性并识别潜在的未观察到的传播路径可能至关重要。在本文中，我们解决这些问题并提出隐藏层识别和重建的方法。我们还探讨了任务难度与描述传播过程发生的整个系统的多层网络结构之间的相互作用。我们的方法源于任意图上易感-感染模型中级联可能性的精确表达式。然后我们表明，通过利用单峰分布的统计特性和描述一系列级联联合可能性的简单启发式方法，可以成功获得隐藏层的存在及其内容的估计，成功率远超过空模型。我们在合成网络和真实世界网络上进行分析，为所提出方法的可行性提供证据。
