基于评分的时空点过程变化点检测与区域定位
Score-Based Change-Point Detection and Region Localization for Spatio-Temporal Point Processes
AI总结：
本文提出一种基于评分的时空点过程变化点检测方法，能够实时定位变化发生的空间区域，提供理论保证和实证验证。
摘要：
我们研究了时空点过程的顺序变化点检测，其中有效的检测不仅需要识别分布变化发生的时间，还需要定位其在空间中的表现位置。虽然经典的最快变化检测方法在检测延迟和虚警率方面提供了强保证，但现有针对点过程数据的方法大多专注于时间变化，并未明确推断受影响的空间区域。我们提出了一种无需假设预变或后变动态参数知识的基于评分的检测框架，该框架在连续的空间时间上联合估计变化时间和变化区域。该方法利用局部化且条件加权的Hyvärinen评分来量化事件层面与名义行为的偏离，并通过预设的空间区域类别的空间时间CUSUM型统计量聚合这些评分。该过程顺序进行，输出停止时间和估计的变化区域，使能够实现实时检测并具有空间可解释性。我们建立了对虚警控制、检测延迟和空间定位准确性的理论保证，并通过模拟和真实世界时空事件数据展示了所提方法的有效性。
英文摘要：
We study sequential change-point detection for spatio-temporal point processes, where actionable detection requires not only identifying when a distributional change occurs but also localizing where it manifests in space. While classical quickest change detection methods provide strong guarantees on detection delay and false-alarm rates, existing approaches for point-process data predominantly focus on temporal changes and do not explicitly infer affected spatial regions. We propose a likelihood-free, score-based detection framework that jointly estimates the change time and the change region in continuous space-time without assuming parametric knowledge of the pre- or post-change dynamics. The method leverages a localized and conditionally weighted Hyvärinen score to quantify event-level deviations from nominal behavior and aggregates these scores using a spatio-temporal CUSUM-type statistic over a prescribed class of spatial regions. Operating sequentially, the procedure outputs both a stopping time and an estimated change region, enabling real-time detection with spatial interpretability. We establish theoretical guarantees on false-alarm control, detection delay, and spatial localization accuracy, and demonstrate the effectiveness of the proposed approach through simulations and real-world spatio-temporal event data.
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