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：我们考虑序列变更检测问题，目标是设计一种方案，用于检测数据流分布参数或泛函$\theta$的任意变化。该方案需具备较小的检测延迟，并在无变化时保证对误报频率的控制。本文描述了一种从序列变更检测到序列估计的简单归约方法：利用置信序列，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为空集时宣告发生变更。我们证明平均运行长度至少为$1/\alpha$，从而得到一种仅需极弱结构假设（因此允许相依观测及非参数分布类）但具有强保证的变更检测方案。我们的方法与Lorden (1971)提出的从变更检测到序列检验的归约思想，以及Shin等人(2022)的电子检测器存在有趣的平行关系。