标题： 高维和非欧几里得数据的序列变化点检测 显示英文标题

标题： Sequential Change-point Detection for High-dimensional and non-Euclidean Data

摘要： 在许多应用中，检测高维或非欧几里得观测序列中的异常事件在实践和科学上具有重要意义。我们研究了一个非参数框架，该框架利用观测值之间的最近邻信息，在在线设置中检测变化。只要可以在样本空间上定义相似性度量，就可以将其应用于任意维度和非欧几里得数据。我们在该框架下考虑了新的检验统计量，与现有检验相比，能够更有效地检测异常事件，同时将错误发现率控制在固定水平。推导了近似新方法平均运行长度的解析公式，以使其快速适用于现代数据集。提供了模拟研究来支持理论结果。所提出的方法通过纽约市出租车数据集的分析进行了说明。 显示英文摘要

摘要： In many applications, it is often of practical and scientific interest to detect anomaly events in a streaming sequence of high-dimensional or non-Euclidean observations. We study a non-parametric framework that utilizes nearest neighbor information among the observations to detect changes in an online setting. It can be applied to data in arbitrary dimension and non-Euclidean data as long as a similarity measure on the sample space can be defined. We consider new test statistics under this framework that can detect anomaly events more effectively than the existing test while keeping the false discovery rate controlled at a fixed level. Analytic formulas approximating the average run lengths of the new approaches are derived to make them fast applicable to modern datasets. Simulation studies are provided to support theoretical results. The proposed approach is illustrated with an analysis of the NYC taxi dataset.