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CAREER: New Change-Point Problems in Analyzing High-Dimensional and Non-Euclidean Data

职业：分析高维和非欧几里得数据的新变点问题

基本信息

批准号：
1848579
负责人：
Hao Chen
金额：
$ 40万
依托单位：
University of California-Davis
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：
2019-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1848579&HistoricalAwards=false
关键词：
CAREER New Change Point Problems

项目摘要

In this big data era, massive data sequences are collected in various scientific fields for studying complicated phenomena over time and space, including neuroscience, epidemiology, social science, computer vision, and astronomy. Change-point analysis is a crucial early step in analyzing these data sequences, such as, to raise an alarm when an abnormal event happens in online data monitoring, and to segment a long sequence into more homogeneous parts for follow-up studies. To accommodate modern applications, the ability to deal with high throughput data and data with complicated structures is becoming a necessity. Parametric methods usually cannot be applied to very high dimensions unless strong assumptions are made to avoid the estimation of a large number of nuisance parameters. This project focuses on developing non-parametric change-point detection methods that are free of strong assumptions and computationally scalable to high dimensional and complex data. This project provides students and researchers with exciting new research problems that have both statistical and scientific importance. The training component for undergraduate and graduate students will prepare new researchers with inter-disciplinary education.This project will develop a new scan statistic framework through a novel adaptation of graph-based methods. The PI has shown that the graph-based approaches scale to high-dimensional and non-Euclidean data, and allow for universal analytic permutation p-value approximations that is decoupled from application-specific modeling, facilitating their applications to large and complicated data sets. Despite the good properties of the graph-based methods, there are still some gaps between its current versions and many modern applications. This project aims to fill those important gaps. In particular, this project will (1) develop new graph-based approaches to effectively integrate information from multiple sources, which is common in many application areas, such as smart homes and smart cities, and seek ways to distribute the new approaches to local centers to avoid the excessive transmission of raw data in a distributed system; (2) develop treatments from the level of constructing the graph to deal with dependent data, which is more effective than a circular block permutation framework developed by the PI earlier; and (3) develop a new framework to provide analytic power approximations to the graph-based methods that kick in for sample sizes in hundreds and thousands even for high-dimensional data and non-Euclidean data, facilitating researchers to make better decisions in real applications. These methodological and theoretical developments will provide better understandings of modern complicated data sequences from diverse fields, which will further advance the understanding of major scientific problems in these fields. The tools developed in this project will be distributed as open source software packages with detailed documentations. This will enhance the collaboration between the statistics community and researchers from broader scientific fields, and make data analysis procedures more transparent.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.

在这个大数据时代，在各个科学领域收集了大量数据序列，用于研究时间和空间上的复杂现象，包括神经科学，流行病学，社会科学，计算机视觉和天文学。变点分析是分析这些数据序列的关键早期步骤，例如，当在线数据监测中发生异常事件时发出警报，以及将长序列分割成更同质的部分以供后续研究。为了适应现代应用，处理高吞吐量数据和具有复杂结构的数据的能力正变得必要。参数方法通常不能应用于非常高的维度，除非做出强有力的假设以避免估计大量的讨厌的参数。该项目的重点是开发非参数变点检测方法，这些方法不需要强假设，并且可以在计算上扩展到高维和复杂的数据。该项目为学生和研究人员提供了令人兴奋的新的研究问题，具有统计和科学的重要性。对本科生和研究生的培训部分将为新的研究人员提供跨学科的教育。该项目将通过对基于图形的方法的新的适应来开发一个新的扫描统计框架。 PI已经表明，基于图的方法可以扩展到高维和非欧几里德数据，并允许通用的解析置换p值近似，与特定于应用程序的建模解耦，便于将其应用于大型和复杂的数据集。尽管基于图的方法具有良好的性能，但其当前版本与许多现代应用之间仍存在一些差距。该项目旨在填补这些重要空白。具体而言，该项目将（1）开发新的基于图形的方法，以有效地整合来自多个来源的信息，这在许多应用领域中是常见的，如智能家居和智能城市，并寻求将新方法分发到本地中心的方法，以避免在分布式系统中过度传输原始数据;（2）从构造图的层次开发处理依赖数据的方法，这比PI早期开发的循环块置换框架更有效;以及（3）开发一个新的框架，为基于图的方法提供分析能力近似，即使对于高维数据和非欧几里德数据，基于图的方法也可以用于数百和数千个样本大小，从而促进研究人员在真实的应用中做出更好的决策。这些方法和理论的发展将提供更好的理解现代复杂的数据序列从不同的领域，这将进一步推进在这些领域的重大科学问题的理解。在这个项目中开发的工具将作为开源软件包分发，并附有详细的文档。这将加强统计界与来自更广泛科学领域的研究人员之间的合作，并使数据分析程序更加透明。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。