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

TL;DR

This paper introduces a likelihood-free, score-based method for real-time change-point detection in spatio-temporal point processes, capable of identifying when and where distributional changes occur in space and time.

Contribution

It proposes a novel joint detection and localization framework that does not rely on parametric assumptions and provides theoretical guarantees for false alarms, delay, and spatial accuracy.

Findings

Effective in real-world data and simulations

Provides simultaneous change detection and spatial localization

Achieves theoretical guarantees on performance metrics

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.