FRG: Collaborative Research: Flexible Network Inference

科学家们一直在研究许多自然系统，将它们视为网络，这个术语用于描述实体的集合及其相互作用。网络在许多领域无处不在，包括流行病学、经济学、社会学、基因组学和生态学等。过去二十年来出现了许多统计模型来描述网络数据。一种常见的模型是潜在空间模型，其中每个实体的行为由其在某些未观察到的（潜在）空间中的位置决定，如果我们知道这些位置，我们就可以完全描述网络的统计行为。虽然这些模型在许多问题中是有用的，但真实的系统往往更加复杂。该项目的目标是通过开发网络分析方法来填补模型与现实之间的差距，即使模型与数据不完全匹配，这些方法仍然表现良好。 该项目的具体目标是提高我们对现有网络分析方法在模型错误指定，异构噪声和不完整或缺失数据下的理解，并开发对这些错误来源具有鲁棒性的新网络方法。 我们认为这两个问题在一个统一的框架下，表示网络的邻接矩阵作为其期望加上条目的噪声，其中包括最流行的网络模型。 在这个框架内，该项目将研究模型错误指定对下游推理的影响，无论是全局推理任务（例如，网络级汇总统计）和本地推理（例如，节点级统计）。该项目的一个核心目标是为网络开发自举和恢复算法，这是经典统计学中两个非常有用的工具，目前还没有完整的网络模拟。另一个核心目标是开发社区成员和节点相似性的更一般概念，允许将鲁棒算法扩展到更广泛的网络模型集合。最后，开发的方法将扩展到多个网络的分析。这些工具结合在一起，将大大扩展网络技术的工具箱，同时考虑到嘈杂和不完整的网络数据和不完善的网络模型的现实。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Scientists have been studying many natural systems by viewing them as networks, a term used to describe collections of entities and their interactions. Networks are ubiquitous in many fields, including epidemiology, economics, sociology, genomics and ecology, to name a few. A number of statistical models have emerged over the last two decades to describe network data. One common type of model is the latent space model, where each entity’s behavior is governed by its position in some unobserved (latent) space, and if we knew these positions, we could fully describe the statistical behavior of the network. While these models have been useful in many problems, real systems tend to be more complicated. The goal of this project is to fill this gap between models and reality by developing network analysis methods that still perform well even when the model does not fully match the data. The specific aims of this project are to improve our understanding of existing network analysis methods under model misspecification, heterogeneous noise, and incomplete or missing data, and to develop novel network methods that are robust to these sources of error. We consider both these problems under one unified framework that represents the adjacency matrix of a network as its expectation plus entry-wise noise, which encompasses most popular network models. Within this framework, the project will examine the effects of model misspecification on downstream inference, both for global inference tasks (e.g., network-level summary statistics) and local inference (e.g., node-level statistics). One core goal of the project is developing bootstrap and resampling algorithms for networks, two extremely useful tools in classical statistics that do not yet have full network analogues. Another core goal is developing more general notions of community membership and node similarity, allowing the extension of robust algorithms to a broader collection of network models. Finally, the methods developed will be extended to the analysis of multiple networks. Taken together, these tools will substantially expand the toolbox of network techniques, while accounting for the realities of noisy and incomplete network data and imperfect network models.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.