LABS：通过前瞻装置扩展二元分割的适用范围
LABS: Extending the scope of binary segmentation via a look-ahead device
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中文总结 AI 辅助
针对二元分割在斜率变化检测中失效的问题，提出前瞻二元分割（LABS），继承其计算速度，在斜率变化场景下达到近最优收敛速率，模拟显示其性能达到先进水平。
中文摘要 AI 辅助
二元分割因快速、描述简单且易于实现，被广泛用于多变点检测。其有效性依赖于一个前提：在每个递归阶段，若当前区间内存在多个真实变点，该过程能识别其中一个真实变点。对于使用CUSUM统计量检测均值变化，这一前提成立，但在某些场景下不成立，尤其是连续分段线性信号的斜率变化检测。我们提出前瞻二元分割（Look-Ahead Binary Segmentation，LABS），该方法对标准二元分割进行了改进：由两个子递归返回的变点定义一个更窄的区间，父估计在该区间上重新评估。LABS继承了标准二元分割的计算速度，当通过阈值法或类Schwarz信息准则选择LABS模型时，在斜率变化信号场景下可达到接近最优的收敛速率$O\{(n\log n)^{1/2}\}$。模拟结果显示，LABS运行快速，且达到了最先进的性能。
英文摘要
Binary segmentation is widely used for multiple change-point detection because it is fast, simple to describe, and simple to implement. Its validity rests on the requirement that, at each recursive stage, the procedure identifies one of the true change-points when several are present in the current interval. This holds for detecting changes in mean using the CUSUM statistic, but fails in some other settings, in particular in slope change detection for continuous piecewise-linear signals. We propose Look-Ahead Binary Segmentation (LABS), a modification in which the change-points returned by the two child recursions define a narrower interval on which the parent estimate is re-evaluated. LABS inherits the computational speed of standard binary segmentation, but achieves the near-optimal consistency rate of $O\{(n\log n)^{1/2}\}$ in the slope-change signal setting when the LABS model is chosen via either thresholding or a Schwarz-like information criterion. Simulations show that LABS is fast and achieves state-of-the-art performance.
