FRG: Collaborative Research: Flexible Network Inference

FRG：协作研究：灵活的网络推理

• 批准号: 2052632
• 负责人: Keith Levin
• 金额: $ 20万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2052632&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Flexible; Network

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.

科学家们一直在研究许多自然系统，将它们视为网络，一个用来描述实体集合及其相互作用的术语。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。在过去的二十年里，出现了许多描述网络数据的统计模型。一种常见的模型类型是潜在空间模型，其中每个实体的行为由其在一些未观察到的（潜在）空间中的位置控制，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都很有用，但实际系统往往更复杂。这个项目的目标是通过开发网络分析方法来填补模型和现实之间的差距，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规范、异构噪声和数据不完整或缺失情况下的理解，并开发对这些错误来源具有鲁棒性的新网络方法。我们在一个统一的框架下考虑这两个问题，该框架将网络的邻接矩阵表示为其期望加上入口噪声，其中包括最流行的网络模型。在此框架内，该项目将检查模型错误规范对下游推理的影响，包括全局推理任务（例如，网络级汇总统计）和局部推理（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重采样算法，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更通用的社区成员和节点相似性概念，从而允许将健壮的算法扩展到更广泛的网络模型集合。最后，所开发的方法将扩展到多个网络的分析。总的来说，这些工具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。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。