AI 中文总结
针对变化前后分布均未知的非参数序贯变化检测问题，提出一类非分区电子检测器，证明其可达到一阶渐近最优检测延迟，适用于多种具体变化场景。
AI 中文摘要
我们研究了一类概率分布（$\boldsymbol{\textit{P}}$）上的序贯变化检测问题，其中变化前和变化后的分布均未知且属于$\boldsymbol{\textit{P}}$。我们不假设$\boldsymbol{\textit{P}}$被预先划分为变化前和变化后的分布族。我们提出一类通用的序贯变化检测器，该检测器通过聚合可能变化点上的点零电子过程，并对候选无变化分布取下确界得到。聚合方案中的权重决定了它们是否能达到平均运行长度（ARL）控制和虚警概率（PFA）控制。在适当假设下，我们证明所提方法达到一阶渐近最优检测延迟。具体例子包括次高斯和有界均值变化、方差未知的高斯均值变化，以及马尔可夫转移矩阵的变化。
英文摘要
We study the problem of sequential change detection over a general class of probability distributions ($\mathcal P$), where both the pre-change and post-change distributions are unknown and belong to $\mathcal P$. We do not assume a pre-specified partition of $\mathcal P$ into pre- and post-change families. We propose a general class of sequential change detectors obtained by aggregating point-null e-processes over possible changepoints and taking an infimum over candidate no-change distributions. The weights in the aggregation scheme determine whether they attain average run length (ARL) control and probability-of-false-alarm (PFA) control. Under suitable assumptions, we prove that our methods achieve first-order asymptotically optimal detection delay. Concrete examples include sub-Gaussian and bounded mean changes, Gaussian mean changes with unknown variance, as well as changes in Markov transition matrices.
