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Offline and Online Change-point Analysis for Large-scale Time Series Data

大规模时间序列数据的离线和在线变点分析

基本信息

批准号：
1916239
负责人：
Jun Li
金额：
$ 10万
依托单位：
Kent State University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2023-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916239&HistoricalAwards=false
关键词：
Offline Online Change point Analysis

项目摘要

Offline or online time series data often involve change points due to the dynamic behavior of the monitored systems. Identifying change points from offline time series data makes parameter estimation and statistical inference efficient by pooling homogeneous observations. Detection of change points from online time series data provides timely snapshots of the monitored system and allows for real-time anomaly detection. Despite its importance, methods available for detecting change points in large-scale offline and online time series data are scarce. This is because a large number of parameters cannot be estimated accurately with a limited number of observations, and parametric models do not fully capture multifarious aspects of data dependence. This project will develop new non-parametric change-point detection methods that incorporate both spatial and temporal dependence without imposing restrictive structural assumptions on large-scale time series data. The proposed methods will span a wide range of topics in applications, including identifying significant genes associated with certain diseases, studying dynamic functional connectivity in resting-state functional magnetic resonance imaging data, and detecting abrupt events such as dissociation of communities, or formation of new communities from social networking platforms. This project will integrate research and education by involving students at different levels, including those from underrepresented groups, and by training the pre-college and high school teachers to improve their knowledge in statistics through new developed courses. The developed methods will be disseminated to biomedical and social scientists through interdisciplinary collaborations and the analysis of first-hand datasets. This project will develop a general factor model framework for spatial and temporal dependence of large-scale time series data. By integrating the framework, this project will provide hypothesis testing and offline change-point estimation of specific parameters, including the population mean and covariance matrix. The proposed methods can be readily modified to incorporate the advantages of both sum-of-squares-norm and max-norm statistics for hypothesis testing. They can be extended from regular binary segmentation methods to other popular change-point estimation methods, such as circular binary segmentation and wild binary segmentation. This project will also provide new stopping rules for online change-point detection of large-scale time series data. An explicit expression for the average run length (ARL) will be derived, so that the level of threshold in stopping rules can be easily obtained with no need to run time-consuming Monte Carlo simulations. The proposed research will derive an upper bound for the expected detection delay (EDD), the expression of which clearly demonstrates the impact of data dimensionality and dependence. This project will extend the current knowledge about change-point detection. For offline change-point detection, the PI will study the possibility of estimating the change point near the boundary in high dimensional settings. For online change-point detection, a comparison will be made between the stopping rule based on the sum-of-squares-norm statistic and the one based on the max-norm statistic, through the derived ARLs and EDDs.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.

离线或在线时间序列数据通常涉及由于被监控系统的动态行为而引起的变化点。从离线时间序列数据中识别变点，通过合并齐次观测值来进行参数估计和统计推断。从在线时间序列数据中检测变化点提供了被监控系统的及时快照，并允许实时异常检测。尽管其重要性，方法可用于检测大规模离线和在线时间序列数据中的变化点是稀缺的。这是因为大量的参数不能用有限数量的观测值准确地估计，并且参数模型不能完全捕获数据依赖性的各种方面。该项目将开发新的非参数变化点检测方法，该方法将空间和时间依赖性结合起来，而不会对大规模时间序列数据施加限制性的结构假设。所提出的方法将涵盖广泛的应用主题，包括识别与某些疾病相关的重要基因，研究静息态功能磁共振成像数据中的动态功能连接，以及检测突发事件，如社区分离或从社交网络平台形成新社区。该项目将把研究和教育结合起来，让不同层次的学生，包括代表性不足群体的学生参与，并培训大学预科和高中教师，通过新开发的课程提高他们的统计知识。将通过跨学科合作和第一手数据集分析，向生物医学和社会科学家传播所开发的方法。本项目将为大规模时间序列数据的空间和时间依赖性开发一个通用因素模型框架。通过整合框架，本项目将提供特定参数的假设检验和离线变点估计，包括总体均值和协方差矩阵。所提出的方法可以很容易地修改，以纳入两个平方和范数和最大范数统计的假设检验的优点。它们可以从常规的二进制分割方法扩展到其他流行的变点估计方法，如循环二进制分割和野生二进制分割。该项目还将为大规模时间序列数据的在线变点检测提供新的停止规则。一个显式的平均游程长度（ARL）的表达式将被导出，因此，在停止规则中的阈值的水平可以很容易地获得，而不需要运行耗时的蒙特卡罗模拟。所提出的研究将得出一个上限的预期检测延迟（EDD），其表达式清楚地表明了数据的维度和依赖性的影响。这个项目将扩展目前的知识变化点检测。对于离线变化点检测，PI将研究在高维设置中估计边界附近的变化点的可能性。对于在线变点检测，将通过推导出的ARL和EDD对基于平方和范数统计的停止规则和基于最大范数统计的停止规则进行比较。该奖项反映了NSF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。