用去噪得分匹配检测数据分布突变，无需假设分布形式。
Sequential Change Point Detection via Denoising Score Matching
- 通过加噪和去噪得分匹配估计数据得分函数。
- 理论证明噪声尺度控制能提升检测能力。
- 适用于高维复杂数据流，适合实时异常监测场景。
序列变化点检测在众多实际应用中至关重要，及时识别分布变化可显著降低不良后果。传统方法通常依赖变化前后分布的参数化密度假设，限制了其在高维复杂数据流中的有效性。本文提出基于得分的CUSUM变化点检测方法，通过注入噪声并应用去噪得分匹配来估计数据分布的得分函数。我们考虑了离线与在线两种得分估计版本。理论分析表明，去噪得分匹配可通过有效控制注入噪声的尺度来增强检测性能。最后，我们在两个合成数据集和一个真实的地震前兆检测任务上验证了该方法的实际有效性，展示了其在挑战性场景下的优越表现。
原文摘要 · Abstract (English)
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.
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