LABS: Extending the scope of binary segmentation via a look-ahead device

2026-08-21

AI Summary

提出了一种改进的二分法（LABS），通过预估机制重新评估父节点估计值，解决了斜率变化检测中的问题，实现了接近最优的一致性速率。

Abstract

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.

Problem

• binary segmentation
• change-point detection
• slope change

Innovation

• Look-Ahead Binary Segmentation
• change-point detection
• slope change detection
• near-optimal consistency rate