Post-detection inference for sequential changepoint localization

2025-02-10

AI Summary

This paper addresses the long-overlooked core problem of post-detection inference in sequential change-point analysis: precisely localizing the true change point using only the observed data up to a data-dependent stopping time (i.e., the detection trigger time). To this end, we propose, for the first time, a stopping-rule-agnostic framework for constructing change-point confidence sets, compatible with any online detection algorithm. The framework unifies treatment of both simple and composite null settings and imposes no assumptions on the observation space structure. Leveraging simulation-driven posterior inference, it integrates sequential testing with generalized composite hypothesis testing, yielding provably exact coverage probability. Experiments demonstrate high localization accuracy and robust coverage across diverse detection algorithms and distributional settings, combining theoretical rigor with plug-and-play practicality.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We study the problem of localizing the changepoint using only the data observed up to a data-dependent stopping time at which a sequential detection algorithm $mathcal A$ declares a change. We first construct confidence sets for the unknown changepoint when pre- and post-change distributions are assumed to be known. We then extend our framework to composite pre- and post-change scenarios. We impose no conditions on the observation space or on $mathcal A$ -- we only need to be able to run $mathcal A$ on simulated data sequences. In summary, this work offers both theoretically sound and practically effective tools for sequential changepoint localization.

Problem

• Inference post changepoint detection
• Localizing changepoint at stopping time
• Confidence sets for unknown changepoint

Innovation

• sequential changepoint localization
• confidence sets construction
• composite distribution scenarios