Network Time Series: From Dynamics to Coevolution

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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.