Sequential Change Point Detection via Denoising Score Matching

TL;DR

This work tackles sequential change-point detection without relying on parametric density assumptions, tackling high-dimensional data streams via denoising score matching to learn the data score and constructing a Hyvärinen-score-based CUSUM statistic. It develops offline and online variants (DSM-CUSUM) that train score models on reference data and, in the online setting, update post-change models with a sliding window, achieving detection with controlled false alarms. Theoretical results quantify how the injected noise scale affects score estimation and detection power, providing WADD bounds that depend on the Fisher divergence between post- and pre-change distributions. Empirically, DSM-CUSUM demonstrates stronger detection capability than baselines on synthetic tasks and a real earthquake-precursor dataset, highlighting its potential for robust, high-dimensional change detection in real-time monitoring contexts.

Abstract

Sequential change-point detection plays a critical role in numerous real-world applications, where timely identification of distributional shifts can greatly mitigate adverse outcomes. Classical methods commonly rely on parametric density assumptions of pre- and post-change distributions, limiting their effectiveness for high-dimensional, complex data streams. This paper proposes a score-based CUSUM change-point detection, in which the score functions of the data distribution are estimated by injecting noise and applying denoising score matching. We consider both offline and online versions of score estimation. Through theoretical analysis, we demonstrate that denoising score matching can enhance detection power by effectively controlling the injected noise scale. Finally, we validate the practical efficacy of our method through numerical experiments on two synthetic datasets and a real-world earthquake precursor detection task, demonstrating its effectiveness in challenging scenarios.

Figures (5)

• Figure 1: Simulation results on score estimation error $\epsilon_{\rm est}(\sigma)$, perturbation error $\epsilon_{\rm pert}(\sigma)$, and distribution change error $\epsilon(\sigma)$ (up to constant scaling factors) for varying values of $\sigma$. The ground-truth data is generated from a $1$D Gaussian mixture with two components.
• Figure 2: Comparison of WADD vs ARL on baseline methods for two synthetic datasets. Left: $2$D data by Gaussian mixtures. Right: $10$D data by deep nets.
• Figure 3: Geophysical signal datasets: comparison of our method (red star) with three baseline methods (dashed lines). All values are normalized to the range $[0, 1]$ for ease of comparison. Domain experts identify the true precursor signals as emerging around early June 2014.
• Figure 4: Comparison of the estimated score function obtained using DSM-CUSUM against the ground-truth for the 2D Gaussian mixture dataset. The results demonstrate that the score models effectively capture the ground-truth score function.
• Figure 5: Visualization of the two datasets. The left column depicts $2$D Gaussian mixture data, while the right column represents $10$D neural network data (visualized using t-SNE).

Theorems & Definitions (12)

• Definition 1
• Lemma 1
• Theorem 1: WADD with offline score estimate
• Theorem 2: WADD with online score estimate
• Remark
• Lemma 2
• proof
• Lemma 3
• proof
• proof : Proof of Lemma \ref{['lem:error']}