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

TL;DR

The paper addresses the problem of real-time change-point detection in spatio-temporal point processes while simultaneously localizing the affected region in continuous space. It introduces ST-Score, a likelihood-free, score-based CUSUM-type framework that uses a localized Hyvärinen score and denoising score matching to learn regime-specific scores, enabling joint inference of the change time $\tau$ and region $\Omega$. The authors establish theoretical guarantees on false alarms, detection delay, and localization accuracy, and validate the approach with synthetic simulations and real-world data from earthquakes and wildfires, showing improved delay and spatial precision over baselines. The work advances actionable spatio-temporal monitoring by providing a scalable, interpretable method for rapid detection and localization with practical impacts in geophysics, natural hazards, and related fields.

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 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.

Figures (8)

• Figure 1: Illustration of the problem setting. After some time $\tau$, the intensity function of the event generation process shifts from $\lambda_0$ to $\lambda_1$ within a confined spatial region $\Omega$.
• Figure 2: Illustrative example of \ref{['lem:level-set']}. A dataset with four events $\{x_i\}_{i=1}^4$, the $x_1$ and $x_2$ have $\Delta(x_i) > 0$ while the $x_3$ and $x_4$ have $\Delta(x_i) < 0$. Their spatial coordinates are indicated by blue and white dots, respectively.
• Figure 3: Detection performance versus average run length (ARL) under different settings. The first two figures are the expected detection delay versus ARL plots; the last two plots are the Jaccard index versus ARL plots. Within these sets of figures, we vary the branching ratio $\alpha$ between $0$ and $0.9$.
• Figure 4: Model performance for varying neighborhood radii ($\delta$). Solid lines represent means; dashed lines represent the standard error of the mean.
• Figure 5: Temporal evolution of the estimated change region across different baselines, with each snapshot corresponding to treating the current time as the stopping time. We assume the true change point $\nu = 0.5$. The first row follows the existing setting, while the last two rows modify the true change region to more complex shapes (cross and bimodal). Gray dots represent event spatial coordinates.

Theorems & Definitions (25)

• Example 1: Homogeneous Poisson Process
• Example 2: Self-exciting Hawkes Process
• Lemma 1
• Remark 1: Online Score Estimation
• Lemma 2: False alarm rate
• Lemma 3: Drift
• Lemma 4: Score differences for Hawkes process
• Corollary 1
• Theorem 1
• proof