Change Point Detection for Data with Network Structure

网络结构数据变点检测

基本信息

批准号：
2210358
负责人：
George Michailidis
金额：
$ 30万
依托单位：
University of Florida
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-08-15 至 2023-10-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210358&HistoricalAwards=false
关键词：
Change Point Detection Data Network

项目摘要

Detecting breaks and anomalies in a mechanism that drives the generation of data represents a critical task, due to numerous applications in high-impact areas including health, social, and engineering sciences. This project aims to advance the state of the art of change point analysis for big and complex data, by developing a simple to implement, yet powerful, scalable algorithmic framework, thus providing new tools to examine high-dimensional, long streams for events of interest. The potential application domains of this project include but not limited to occurrence of seizure in brain connectivity data sets, coordinated market and other systemic failures in economic and finance data, and identification of orchestrated malicious activities in computer network streams. The developed algorithms and methodology will be implemented in open-source software, while curated data sets will be made available to the community for use in change point analysis investigations. The project will offer multiple unique opportunities for interdisciplinary research training of the future generation of statisticians and for further enhancement of diversity in mathematical sciences.To achieve the stated goals, the project (i) develops a unified detection framework for change points in complex statistical models for network and high dimensional time streams and (ii) provides a rigorous theoretical analysis of their accuracy in the form of consistency, finite sample bounds, and asymptotic distributions for the change points and other model parameters. The framework leverages a simple, easy to implement two-step strategy, wherein the first step one selects windows of the time series of appropriate length and using a standard exhaustive search strategy identifies at most a single change point in each of them. In the second step, a second search based on a global information criterion is employed to eliminate spurious change points. The strategy exhibits linear complexity in time (and thus matches the fastest available in the literature), yet is simple to implement and theoretically analyze, in particular for complex statistical models that exhibit network and low rank structure. Further, the following issues are rigorously addressed: (i) conditions of identifiability of the model parameters and the change points and (ii) probabilistic guarantees and uncertainty quantification for them in the presence of high dimensionality, network structure, temporal dependence, as well as dependence across data streams.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.

由于在健康，社会和工程科学在内的高影响力领域的应用，驱动数据生成的机制中检测突破和异常是一项关键任务。该项目旨在通过开发一个简单但功能强大，可扩展的算法框架来推动大和复杂数据的变化点分析的状态。该项目的潜在应用领域包括但不限于大脑连通性数据集的癫痫发作，经济和金融数据中的其他系统性失败以及计算机网络流中精心策划的恶意活动的识别。开发的算法和方法将在开源软件中实施，而策划的数据集将提供给社区以供更改点分析调查使用。该项目将为未来一代统计学家的跨学科研究培训提供多个独特的机会，并进一步增强了数学科学的多样性。为了实现既定的目标，该项目（i）为复杂统计模型中的变更点开发了一个统一的检测框架对于网络和高维时流以及（ii），以一致性，有限的样本界限和更改点和其他模型参数的渐近分布形式提供了严格的理论分析。该框架利用一个简单，易于实现的两步策略，其中第一步选择了适当长度的时间序列的窗口，并使用标准的详尽搜索策略最多可以标识每个变化点。在第二步中，采用了基于全球信息标准的第二次搜索来消除虚假的变化点。该策略在时间上表现出线性复杂性（因此与文献中最快的可用性相匹配），但易于实现和理论上分析，特别是对于展示网络和低级结构的复杂统计模型而言。此外，严格解决以下问题：（i）模型参数和变更点的可识别性条件以及（ii）在存在高维度，网络结构，时间依赖性以及概率保证和不确定性量化的情况下跨数据流的依赖性。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评论标准来评估值得支持的。