论文标题
电子指 - 检测器：用于顺序更改检测的非参数框架
E-detectors: a nonparametric framework for sequential change detection
论文作者
论文摘要
顺序更改检测是各种应用程序的经典问题。但是，大多数先前的工作都是参数性的，例如，专注于指数家庭。我们开发了一个从根本上进行新的和一般的框架，以进行顺序变化检测，当时变更和后分布是非参数指定的（因此是复合）的。我们的程序具有平均运行长度（误报频率）上的干净，非反应界限。在某些非参数案例（例如次高斯或次指数）中，我们还在更改点后在检测延迟上提供了近乎最佳的界限。我们介绍的主要技术工具称为\ emph {e-detector}，该工具由E-Prococeses的总和（非负超级智能的基本概括）组成，这些概括是连续启动的。我们首先介绍简单的Shiryaev-Roberts和Cusum风格的电子解放器，然后展示如何设计其混合物以达到统计和计算效率。可以实例化我们的e-detector框架以恢复基于经典的可能性问题的程序，并为许多非参数问题产生第一种变更检测方法。作为一个运行的示例，我们解决了检测无i.i.d的有界随机变量变化的问题。假设，并应用了在多个赛季中跟踪篮球队的表现。
Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework for sequential change detection when the pre- and post-change distributions are nonparametrically specified (and thus composite). Our procedures come with clean, nonasymptotic bounds on the average run length (frequency of false alarms). In certain nonparametric cases (like sub-Gaussian or sub-exponential), we also provide near-optimal bounds on the detection delay following a changepoint. The primary technical tool that we introduce is called an \emph{e-detector}, which is composed of sums of e-processes -- a fundamental generalization of nonnegative supermartingales -- that are started at consecutive times. We first introduce simple Shiryaev-Roberts and CUSUM-style e-detectors, and then show how to design their mixtures in order to achieve both statistical and computational efficiency. Our e-detector framework can be instantiated to recover classical likelihood-based procedures for parametric problems, as well as yielding the first change detection method for many nonparametric problems. As a running example, we tackle the problem of detecting changes in the mean of a bounded random variable without i.i.d. assumptions, with an application to tracking the performance of a basketball team over multiple seasons.
