DMS-EPSRC: Change-Point Detection and Localization in High Dimensions: Theory and Methods

统计变化点分析关注的是在一段时间内收集测量数据时识别数据的突然变化。一个根本的挑战是，如何区分与基础数据生成模型中结构性但可能微妙的变化相对应的变化和可能仅仅是随机波动造成的变化。变化点模型自然出现在各种科学和工业应用中，包括安全监测、神经成像、金融交易、生态统计、气候变化、医疗监测、传感器网络、疾病爆发风险评估、流感趋势分析、遗传学等。尽管从业者可以使用许多完善的方法来对变化点问题进行统计分析，但主流框架存在重要的局限性：(i)它通常依赖于传统的建模假设，其表达能力有限，不足以捕捉现代数据集的规模和固有复杂性；（ii）它不能直接适用于非标准数据类型，如网络或图结构信号。该项目的总体目标是为各种新的变化点设置开发新的理论、可行的方法和软件工具，以解决复杂的大数据问题，并推进变化点分析的统计推断实践。除了科学成果之外，该项目还将汇集不同的研究人员，其中一些来自统计学中代表性不足的群体。该项目将为研究生提供研究培训机会。项目主要研究目标有三个：(1)从简单的单变量平均变点模型到涉及高维参数的协方差、回归模型、动态单层和多层网络模型等更复杂的设置，推导出统计上最优的、计算效率最高的变化点存在检测和位置估计方法；(2)推导出图结构信号中变化点检测和定位的新保证和方法；(3)开发复杂数据流中最优顺序变化点分析方法。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。

Statistical change point analysis is concerned with identifying abrupt changes in data when measurements are collected over time. A fundamental challenge is to discriminate among changes corresponding to structural, but possibly subtle, variations in the underlying data generative model from those that may simply be due to random fluctuations. Change point models arise naturally in a variety of scientific and industrial applications, including security monitoring, neuroimaging, financial trading, ecological statistics, climate change, medical monitoring, sensor networks, disease outbreak risk assessment, flu trend analysis, genetics and many others. Though a host of well-established methods for the statistical analysis of change point problems is available to practitioners, the prevailing framework suffers from important limitations: (i) it often relies on traditional modeling assumptions of limited expressive power that are inadequate to capture the size and inherent complexity of modern datasets and (ii) it is not directly applicable to non-standard data types, such as networks or graph-structured signals. The broad goal of this project is to develop novel theories, practicable methods, and software tools for a variety of new change point settings to tackle complex, big data problems and advance the practice of statistical inference for change-point analysis. In addition to its scientific output, the project will bring together a diverse group of researchers, some from underrepresented groups in Statistics. The project will provide research training opportunities for graduate students.The project includes three main research aims: (1) to derive statistically optimal and computationally efficient procedures for detecting the presence and estimating the positions of change points in various offline high-dimensional statistical models, ranging from simple univariate mean change point models to more complicated settings involving high-dimensional parameters, such covariance covariances, regression models, dynamic single and multi-layered network models; (2) to derive novel guarantees and methods for change point detection and localization in graph-structured signals; and (3) to develop methods for optimal sequential change point analysis in complex 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.