The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d data, focuses on asymptotic analysis, does not present theoretical guarantees on the trade-off between detection accuracy and detection delay, or is only suitable for detecting single change points. In this work, we study the online change point detection problem for linear dynamical systems with unknown dynamics, where the data exhibits temporal correlations and the system could have multiple change points. We develop a data-dependent threshold that can be used in our test that allows one to achieve a pre-specified upper bound on the probability of making a false alarm. We further provide a finite-sample-based bound for the probability of detecting a change point. Our bound demonstrates how parameters used in our algorithm affect the detection probability and delay, and provides guidance on the minimum required time between changes to guarantee detection.

翻译：在线变点检测问题的目标是检测时间序列属性的突然变化，并理想地在变化发生后尽快完成检测。现有关于在线变点检测的研究或假设数据独立同分布，或侧重渐近分析，或未给出检测精度与检测延迟之间权衡的理论保证，或仅适用于检测单一变点。本文研究动力学未知的线性动力系统的在线变点检测问题，其中数据存在时间相关性且系统可能存在多个变点。我们提出一种数据依赖的阈值，可应用于所设计的检验中，使得虚警概率能够被预设上界所约束。进一步地，我们给出变点检测概率的有限样本界。该界揭示了算法参数对检测概率和延迟的影响，并为保证检测所需的两次变化间最小时间间隔提供了指导。