Score-Based Change-Point Detection and Region Localization for Spatio-Temporal Point Processes

2026-02-04

AI Summary

Existing methods for change-point detection in spatiotemporal point processes often focus solely on the temporal dimension, making it difficult to localize the precise spatial regions where changes occur. This work proposes a likelihood-free, nonparametric framework for joint spatiotemporal change-point detection. By leveraging a locally weighted conditional Hyvärinen score to quantify event anomalies and integrating it with a spatiotemporal CUSUM-type cumulative sum statistic, the method enables simultaneous inference of both the timing and spatial location of changes in continuous space. To the best of our knowledge, this is the first approach that combines conditional weighted Hyvärinen scoring with a spatiotemporal CUSUM mechanism, offering strong theoretical guarantees—including controllable false alarm rates, bounded detection delay, and localization accuracy—while maintaining spatial interpretability. The efficacy of the proposed method is demonstrated through extensive simulations and real-world data experiments.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

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 Hyv\"arinen 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.

Problem

• change-point detection
• spatio-temporal point processes
• region localization
• spatial interpretability
• sequential detection

Innovation

• score-based detection
• spatio-temporal point processes
• change-point localization
• Hyvärinen score
• CUSUM statistic