Sketching for Sequential Change-Point Detection
This provides an efficient method for anomaly detection in high-dimensional data streams, with applications in solar flare and power network monitoring, though it appears incremental as it builds on existing sketching and GLR approaches.
The paper tackles sequential change-point detection in high-dimensional signals using linear sketches with generalized likelihood ratio statistics, deriving theoretical approximations for performance metrics that show high accuracy in simulations and demonstrating little performance loss compared to non-sketching methods when signal strength and sketch count are sufficient.
We study sequential change-point detection procedures based on linear sketches of high-dimensional signal vectors using generalized likelihood ratio (GLR) statistics. The GLR statistics allow for an unknown post-change mean that represents an anomaly or novelty. We consider both fixed and time-varying projections, derive theoretical approximations to two fundamental performance metrics: the average run length (ARL) and the expected detection delay (EDD); these approximations are shown to be highly accurate by numerical simulations. We further characterize the relative performance measure of the sketching procedure compared to that without sketching and show that there can be little performance loss when the signal strength is sufficiently large, and enough number of sketches are used. Finally, we demonstrate the good performance of sketching procedures using simulation and real-data examples on solar flare detection and failure detection in power networks.