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

2026-05-01

AI Summary

This work proposes Pi-Change, a novel multiple changepoint detection algorithm that incorporates time-varying prior information into the dynamic programming framework of PELT in an interpretable manner, while preserving its computational efficiency. Traditional methods often neglect prior knowledge about changepoint locations, limiting their performance in complex scenarios. Pi-Change addresses this by introducing a time-adaptive penalty term that guides the search for changepoints, effectively suppressing spurious detections lacking prior support. The method maintains the pruning rules essential to PELT’s speed and demonstrates robustness to misspecified priors. Empirical evaluations on synthetic data and three real-world time series show significant improvements in detection accuracy and enable quantitative analysis of delayed structural changes triggered by external events.

Abstract

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.

Problem

• change point detection
• prior information
• multiple change points
• time series
• contextual information

Innovation

• change point detection
• prior-informed inference
• time-varying penalty
• PELT algorithm
• multiple change points