Network Time Series: From Dynamics to Coevolution

在过去的几年里，许多研究领域的真实网络数据量以及对人们日常生活的影响都大幅增加。一个越来越重要的领域是网络时间序列。一些例子包括随时间演化的网络（动态或时间网络），或动态与底层网络结构紧密相连的网络中节点上的时间序列;以及动态网络上的时间序列，其中两种结构共同演化。该项目的具体应用包括社会联系因社会动态而变化的社交网络、顶点特定流（如受其他顶点影响的文本）、功能磁共振成像信号的大脑功能连接网络和大脑结构连接网络的神经科学或空间网络上移民和经济流的社会学和城市规划。尽管在过去的十年中，协调一致的活动，严格的理解网络时间序列模型及其在各个领域的适用性仍然是具有挑战性的，由于宏观结构的复杂出现，通过微观网络组件之间的相互作用规则。该项目的目的是开发网络时间序列的一般理论基础，以告知统计方法的应用以及在实践中的计算技术，同时由PI与上述领域的领域科学家合作指导。此外，该项目将有助于培养学生与设想的数据科学实验室，部分填充从这项工作提供垂直整合的研究经验的项目。 该项目有三个主要支柱，按复杂程度顺序排列。(1)网络调制时间序列。重点是一个潜在的，可能是潜在的静态网络结构的多变量节点时间序列。受近年来网络向量自回归研究的启发，本文研究了混沌模型的网络因子和传播，作为其上级替代和扩展。模型的特殊情况包括社交网络中的意见动态以及神经科学中的Hodgkin-Huxley和FitzHugh-Nagumo模型的网络版本。受城市规划应用的启发，这些模型的空间版本将通过大型网络渐近进行研究。(2)由潜在的多变量时间序列驱动的动态网络。 PI将利用一般时间序列方法和途径进行系统分析，特别是离散值时间序列。时间迁移和经济流网络形成了一个目标应用领域。(3)共同发展的网络。PI研究多变量时间序列受底层网络影响的场景中的网络模型，而底层网络本身也受多变量时间序列的影响。PI将开发数学技术来理解各种突出的现象，包括自激的作用（节点与邻居交互的次数越多，该邻居在未来的影响力（包括创建新连接）就越大）该奖项反映了NSF的法定使命，并通过使用基金会的智力价值进行评估，更广泛的影响审查标准。

The last few years have seen a large increase both in the amount of data on real-world networks in numerous research areas and the impact in people’s daily lives. One increasingly important field is in an area called network time series. Some examples include networks that evolve over time (dynamic or temporal networks), or time series over nodes in a network whose dynamics is intricately tied to the underlying network structure; and time series over dynamic networks where the two structures coevolve. Applications specific to this project include social networks with social connections changing owing to social dynamics, vertex specific streams such as text influenced by other vertices, neuroscience with brain functional connectivity networks from fMRI signals and brain structural connectivity networks or sociology and urban planning with migration and economic flows over spatial networks. Despite concerted activity over the last decade, rigorous understanding of network time series models and their applicability in various domains is still challenging owing to the complex emergence of macroscopic structure through microscopic interaction rules between individual network components. The aim of this project is to develop general theoretical foundations for network time series to inform the application of statistical methodology as well as computational techniques in practice whilst being guided by PIs’ collaborations with domain scientists in the areas mentioned above. Additionally, the project will contribute to the training of students with an envisioned data science lab, populated in part by projects from this work providing vertical integration of research experiences. There are three major pillars to this project, arranged sequentially in order of complexity. (1) Network modulated time series. The focus is on multivariate nodal time series with an underlying, possibly latent static network structure. Motivated by recent work on network vector autoregressions, network factor and propagation of chaos models are studied as superior alternatives and extensions. Special cases of the models include opinion dynamics in social networks and network versions of Hodgkin-Huxley and FitzHugh-Nagumo models in neuroscience. Motivated by applications in urban planning, spatial versions of these models will be studied through large network asymptotics. (2) Dynamic networks driven by possibly latent multivariate time series. The PIs will work on their systematic analysis leveraging general time series methods and approaches, especially for discrete-valued time series. Temporal migration and economic flow networks form one targeted area of applications. (3) Co-evolving networks. The PIs study Network models in the scenario where multivariate time series are affected by the underlying network, which itself is affected by the multivariate time series. The PIs will develop mathematical techniques to understand various salient phenomena including the role of self-excitation (the greater the number of times a node interacts with a neighbor the higher the influence this neighbor has in the future including the creation of new connections) and information decay.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.