We propose an efficient online kernel Cumulative Sum (CUSUM) method for change-point detection that utilizes the maximum over a set of kernel statistics to account for the unknown change-point location. Our approach exhibits increased sensitivity to small changes compared to existing methods, such as the Scan-B statistic, which corresponds to a non-parametric Shewhart chart-type procedure. We provide accurate analytic approximations for two key performance metrics: the Average Run Length (ARL) and Expected Detection Delay (EDD), which enable us to establish an optimal window length on the order of the logarithm of ARL to ensure minimal power loss relative to an oracle procedure with infinite memory. Such a finding parallels the classic result for window-limited Generalized Likelihood Ratio (GLR) procedure in parametric change-point detection literature. Moreover, we introduce a recursive calculation procedure for detection statistics to ensure constant computational and memory complexity, which is essential for online procedures. Through extensive experiments on simulated data and a real-world human activity dataset, we demonstrate the competitive performance of our method and validate our theoretical results.

翻译：我们提出了一种高效的在在线核累计和（CUSUM）方法用于变点检测，该方法利用一组核统计量的最大值来处理未知的变点位置。与现有方法（例如对应于非参数休哈特控制图型程序的Scan-B统计量）相比，我们的方法对小变化具有更高的敏感性。我们为两个关键性能指标提供了精确的解析近似值：平均运行长度（ARL）和期望检测延迟（EDD），这使我们能够建立关于ARL对数量级的最优窗口长度，以确保相对于具有无限记忆的预言程序而言功率损失最小。这一发现与参数变点检测文献中窗口限制广义似然比（GLR）程序的经典结果相呼应。此外，我们引入了一种检测统计量的递归计算程序，以确保恒定计算和内存复杂度，这对于在线程序至关重要。通过在模拟数据和真实世界人类活动数据集上的广泛实验，我们展示了我们方法的竞争性能，并验证了我们的理论结果。