发表机构
Augusta University; Toronto Metropolitan University; Princeton University（奥古斯塔大学; 多伦多都会大学; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对经典CUSUM无法仅用有限样本计算对数似然比的问题，提出无需训练的DI-SCUSUM检测器，在模拟及MNIST、Oxford-IIIT Pet数据集上，其检测延迟显著低于SCUSUM，性能接近似然比CUSUM。
AI 中文摘要
经典CUSUM算法依赖于基础分布的对数似然比，而该对数似然比通常无法仅通过有限的变化前和变化后样本计算得到。我们提出了一种无需训练的检测器：扩散积分得分CUSUM（DI-SCUSUM）。我们向样本中添加高斯噪声以形成两个平滑的密度估计，并精确计算它们的Hyvärinen得分，无需训练得分网络。对于每个传入的观测值，我们采样一个扩散时间、扰动该观测值，并使用重要性加权的得分差作为DI-SCUSUM递归中的增量。在观测值遵循固定经验分布的假设下，变化后的平均增量与平滑后变化后分布和平滑后变化前经验分布之间的Kullback-Leibler（KL）散度成正比。我们建立了指数级的虚警缩放关系和一阶延迟界，对于固定阈值和增量缩放，该延迟界与KL散度成反比。在校准的各向异性高斯模拟中，DI-SCUSUM几乎与似然比CUSUM的性能相当，且相对于基于得分的CUSUM，其测得的检测延迟降低了约91%。在MNIST和Oxford-IIIT Pet数据集上，DI-SCUSUM在相当的虚警水平下，也比SCUSUM具有更低的经验条件检测延迟。
英文摘要
Classical CUSUM relies on the log-likelihood ratio of the underlying distributions, which cannot generally be computed from finite pre- and post-change samples alone. We propose diffusion-integrated score CUSUM (DI-SCUSUM), a training-free detector. We add Gaussian noise to the samples to form two smooth density estimates and calculate their Hyvärinen scores exactly, without training a score network. For each incoming observation, we sample a diffusion time, perturb the observation, and use the importance-weighted score difference as an increment in the DI-SCUSUM recursion. Under the assumption that observations follow the fixed empirical distributions, the post-change mean increment is proportional to the Kullback-Leibler (KL) divergence from the smoothed post-change to the smoothed pre-change empirical distribution. We establish exponential false-alarm scaling and a first-order delay bound that, for a fixed threshold and increment scaling, is inversely proportional to the KL divergence. In the calibrated anisotropic Gaussian simulation, DI-SCUSUM nearly matches likelihood-ratio CUSUM and reduces the measured detection delay by about 91% relative to score-based CUSUM. On MNIST and Oxford-IIIT Pet, DI-SCUSUM also has lower empirical conditional detection delay than SCUSUM at comparable false-alarm levels.
