arXiv:2605.01003stat.MEcs.LG2026-05

用先验信息指导多变化点检测,提升准确性与可解释性。

Pi-Change: A Prior-Informed Multiple Change Point Detection Algorithm

  • 通过时变惩罚项融合先验位置信息
  • 在模拟和真实数据中减少虚假变化点
  • 适合有外部事件或异质机制的场景

统计变化点(CP)检测方法通常依赖似然推断,忽略观测序列外的合理变化点位置上下文信息。尽管信息性先验可自然融入此类信息,但通用且计算高效的多变化点检测方法仍不足。为此,我们提出先验引导的变化点检测算法(Pi-Change),通过时变惩罚项引入变化点位置的先验信息。我们证明该惩罚项可嵌入剪枝精确线性时间(Pruned Exact Linear Time, PELT)框架,在保持动态规划递推关系与剪枝规则的前提下实现高效多变化点检测。在多个模拟研究及三个时间序列应用中,Pi-Change有效抑制了无先验支持的虚假变化点,对先验误设具有鲁棒性,并提升了检测精度。更广泛地,该方法通过计算高效且可解释的方式,将部分先验知识融入多变化点检测,适用于变化点由异质机制引发或与已知外部事件相关的情境,有助于量化事件与结构变化之间的时间延迟。

原文摘要 · Abstract (English)

Statistical change point (CP) detection methods typically rely on likelihood-based inference and ignore contextual information about plausible CP locations beyond the observed sequence. Although informative priors provide a natural way to incorporate such information, general and computationally efficient methods for doing so are lacking, especially for multiple CP detection. To address this gap, we propose a prior-informed CP detection algorithm (Pi-Change) that incorporates prior information on CP locations through a time-varying penalty term. We prove that the proposed penalty can be embedded in the Pruned Exact Linear Time framework while preserving the dynamic programming recursion and pruning rule required for efficient multiple CP detection. Across simulation studies and three time-series applications, Pi-Change discourages spurious CPs unsupported by prior information, remains robust to prior misspecification, and improves detection accuracy. More broadly, Pi-Change extends multiple CP detection beyond purely data-driven fitting by incorporating partial prior knowledge in a computationally efficient and interpretable way. It is particularly useful when CPs arise from heterogeneous mechanisms or are associated with known external events, helping quantify the delay between an event and the resulting structural change.

变化点检测先验信息时间序列高效算法

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