Detecting abrupt changes in real-time data streams from scientific
simulations presents a challenging task, demanding the deployment of accurate
and efficient algorithms. Identifying change points in live data stream
involves continuous scrutiny of incoming observations for deviations in their
statistical characteristics, particularly in high-volume data scenarios.
Maintaining a balance between sudden change detection and minimizing false
alarms is vital. Many existing algorithms for this purpose rely on known
probability distributions, limiting their feasibility. In this study, we
introduce the Kernel-based Cumulative Sum (KCUSUM) algorithm, a non-parametric
extension of the traditional Cumulative Sum (CUSUM) method, which has gained
prominence for its efficacy in online change point detection under less
restrictive conditions. KCUSUM splits itself by comparing incoming samples
directly with reference samples and computes a statistic grounded in the
Maximum Mean Discrepancy (MMD) non-parametric framework. This approach extends
KCUSUM's pertinence to scenarios where only reference samples are available,
such as atomic trajectories of proteins in vacuum, facilitating the detection
of deviations from the reference sample without prior knowledge of the data's
underlying distribution. Furthermore, by harnessing MMD's inherent random-walk
structure, we can theoretically analyze KCUSUM's performance across various use
cases, including metrics like expected delay and mean runtime to false alarms.
Finally, we discuss real-world use cases from scientific simulations such as
NWChem CODAR and protein folding data, demonstrating KCUSUM's practical
effectiveness in online change point detection.

通过引入基于核的累加和（KCUSUM）算法，我们扩展了传统累加和（CUSUM）方法，使之具备了针对高容量数据场景下在线变点检测的能力，并在仅有参考样本的情况下，通过与参考样本的比较来检测数据中与参考样本的偏离情况，从而在实时数据流中检测突变。

一种基于 KCUSUM 的实时自适应采样变点检测算法评估

An Evaluation of Real-time Adaptive Sampling Change Point Detection  Algorithm using KCUSUM

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.

在线线性动力系统中的变点检测方法，解决了时间序列属性突变检测的问题，包括未知动力学、时间相关性和多个变点时的检测准确度和延迟的理论保证。