基于扩散积分分数的快速变化检测 DI-SCUSUM

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Abstract: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.

Subjects:	Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as:	arXiv:2610.12200 [stat.ML]
	(or arXiv:2610.12200v1 [stat.ML] for this version)
	https://doi.org/10.48550/arXiv.2610.12200 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Mohammadreza Maleki [view email]
[v1] Thu, 8 Oct 2026 15:53:36 UTC (331 KB)