论文标题
通过最佳加权$ \ ell_2 $ divergence检测顺序更改检测
Sequential Change Detection by Optimal Weighted $\ell_2$ Divergence
论文作者
论文摘要
我们提出了一个新的非参数统计量，称为$ \ ell_2 $ divergence，基于用于顺序变化检测的经验分布。我们首先要构建称重的$ \ ell_2 $ divergence作为两样本测试和更改检测的基本构建块。事实证明，提出的统计量可以在离线设置中达到最佳样本复杂性。然后，我们使用称重$ \ ell_2 $ divergence研究顺序变化检测，并表征基本性能指标，包括平均运行长度（ARL）和预期检测延迟（EDD）。我们还提出了实用算法，以找到处理高维数据和最佳权重的最佳投影，这对于快速检测至关重要，因为在这种情况下，变化后样本不多。提供了仿真结果和实际数据示例，以验证提出方法的良好性能。
We present a new non-parametric statistic, called the weighed $\ell_2$ divergence, based on empirical distributions for sequential change detection. We start by constructing the weighed $\ell_2$ divergence as a fundamental building block for two-sample tests and change detection. The proposed statistic is proved to attain the optimal sample complexity in the offline setting. We then study the sequential change detection using the weighed $\ell_2$ divergence and characterize the fundamental performance metrics, including the average run length (ARL) and the expected detection delay (EDD). We also present practical algorithms to find the optimal projection to handle high-dimensional data and the optimal weights, which is critical to quick detection since, in such settings, there are not many post-change samples. Simulation results and real data examples are provided to validate the good performance of the proposed method.
