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

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.

💡 Research Summary

The paper addresses the problem of sequential change‑point detection in spatio‑temporal point processes (STPPs) where the change is confined to an unknown spatial region. Classical quickest detection methods focus solely on the time dimension and assume known parametric models, which limits their applicability to modern event‑type data such as earthquakes, wildfires, or crime incidents that exhibit both temporal and spatial structure. The authors propose a likelihood‑free, score‑based framework that simultaneously estimates the change time τ and the affected region Ω without requiring explicit knowledge of the pre‑change (λ₀) or post‑change (λ₁) intensity functions.

The core of the method is a localized, conditionally weighted Hyvärinen score. For each observed event x = (t,s), the Hyvärinen score evaluates the discrepancy between the observed event and the pre‑change model using the gradient of the log‑density. By applying a space‑time weight function, the score becomes sensitive to local deviations while remaining robust in sparse regions. These event‑level scores are then aggregated over a candidate spatial region Ω through a spatio‑temporal CUSUM‑type statistic:

 Wₜ(Ω) = max₀≤τ≤t