Diffusion-integrated scores speed up detecting data changes in real time
Quickest Change Detection with Diffusion-Integrated Scores
Machine Learning
Summary
Detecting when data changes quickly is important but can be hard because typical methods need detailed knowledge about the data. This paper presents a new method called DI-SCUSUM that uses added noise and mathematical scores to spot changes without training on data. Their method works well by measuring how different the noisy versions of data before and after changes are and does this faster than other score-based techniques. They tested it on both simulated and real image data, showing it detects changes with less delay and similar false alarms.
What this means in practice
- •For industrial monitoring teams: Improve real-time fault detection by using DI-SCUSUM to identify shifts in sensor data without requiring extensive model training.
- •For cybersecurity analysts: Detect subtle changes in network traffic patterns faster with DI-SCUSUM to quickly respond to intrusions or anomalies.
Authors
Arman Adibi, Mohammadreza Maleki, Sanjeev Kulkarni, H. Vincent Poor
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.