Quickest Change Detection with Diffusion-Integrated Scores
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.
Related
- Robust Quickest Change Detection with Cost-Efficient Experiment Design and Unknown Post-Change Model
- Quickest Change-point Detection in Generalized Linear Models with Variational Estimation
- A Mixture-of-Experts Framework for Multi-Stream Quickest Change Detection
- Pollak's Minimax Quickest Change Detection: Non-Asymptotic Optimality
- QD-PINN:A Physics-Informed Neural Network Approach to Bayesian Quickest Detection in High-Dimensional Diffusions
BibTeX
@misc{adibi2026quickest,
title = {{Quickest Change Detection with Diffusion-Integrated Scores}},
author = {Arman Adibi and Mohammadreza Maleki and Sanjeev Kulkarni and H. Vincent Poor},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12200},
eprint = {2610.12200},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12200},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quickest Change Detection with Diffusion-Integrated Scores
AU - Arman Adibi
AU - Mohammadreza Maleki
AU - Sanjeev Kulkarni
AU - H. Vincent Poor
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12200
UR - https://arxiv.org/abs/2610.12200
AB - 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.
ER -