We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new $(1-\alpha)$-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least $1/\alpha$, resulting in a change detection scheme with minimal structural assumptions~(thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. Our approach bears an interesting parallel with the reduction from change detection to sequential testing of Lorden (1971) and the e-detector of Shin et al. (2022).

翻译：我们考虑序贯变化检测问题，其目标是设计一种方案，用于检测数据流分布中参数或泛函$\theta$的任何变化，该方案需具有较小的检测延迟，同时在无变化时保证对误报频率的控制。本文描述了一种通过置信序列将序贯变化检测简化为序贯估计的简单方法：我们在每个时间步启动一个新的$(1-\alpha)$置信序列，当所有活跃置信序列的交集变为空时，宣告变化发生。我们证明平均运行长度至少为$1/\alpha$，由此得到一种结构假设极少的（因此允许依赖观测和非参数分布类别）但具有强保障的变化检测方案。我们的方法与Lorden (1971)将变化检测简化为序贯检验的方法以及Shin等人(2022)的e-检测器存在有趣的平行关系。