具有校准和无记忆误检率的顺序多变量变化检测
Sequential Multivariate Change Detection with Calibrated and Memoryless False Detection Rates
摘要：
适当地响应于顺序变化检测器的检测需要知道在没有变化的情况下假阳性发生的速率。设置检测阈值以实现期望的假阳性率是具有挑战性的。现有的作品诉诸于设置时不变的阈值，专注于在没有变化的情况下，检测器的预期运行时间，无论是从下面松散地绑定它或直接针对它，但与渐近参数，我们显示在实践中造成重大的误校准。我们提出了一种基于模拟的方法来设置随时间变化的阈值，允许所需的预期运行时间被准确地定位，同时还保持跨时间步长的误报率恒定。虽然阈值设置的方法是度量不可知的，我们展示了如何使用流行的二次时间MMD估计的成本可以减少从$O(N^2B)$到$O(N^2+NB)$在配置过程中，从$O(N^2)$到$O(N)$在操作过程中，其中$N$和$B$分别是参考和引导样本的数量。
英文摘要：
Responding appropriately to the detections of a sequential change detector requires knowledge of the rate at which false positives occur in the absence of change. Setting detection thresholds to achieve a desired false positive rate is challenging. Existing works resort to setting time-invariant thresholds that focus on the expected runtime of the detector in the absence of change, either bounding it loosely from below or targeting it directly but with asymptotic arguments that we show cause significant miscalibration in practice. We present a simulation-based approach to setting time-varying thresholds that allows a desired expected runtime to be accurately targeted whilst additionally keeping the false positive rate constant across time steps. Whilst the approach to threshold setting is metric agnostic, we show how the cost of using the popular quadratic time MMD estimator can be reduced from $O(N^2B)$ to $O(N^2+NB)$ during configuration and from $O(N^2)$ to $O(N)$ during operation, where $N$ and $B$ are the numbers of reference and bootstrap samples respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
