Sequential Change Point Detection via Denoising Score Matching

TL;DR

This paper introduces a score-based CUSUM method for sequential change-point detection that leverages denoising score matching to improve detection in high-dimensional, complex data streams, validated through synthetic and real-world experiments.

Contribution

It proposes a novel score-based change-point detection approach using denoising score matching, addressing limitations of parametric methods in complex data environments.

Findings

Enhanced detection power through noise scale control

Effective in synthetic data scenarios

Successful application to earthquake precursor detection

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.