Optimal Online Change Detection via Random Fourier Features
This addresses the problem of detecting changes in data streams without needing pre-change training data or window parameters, which is incremental but improves efficiency and usability for real-time monitoring applications.
The paper tackles online non-parametric change point detection in multivariate data streams by introducing a kernel-based sequential testing procedure using random Fourier features, achieving logarithmic time and space complexity, and proving optimal detection delay with competitive performance in numerical studies.
This article studies the problem of online non-parametric change point detection in multivariate data streams. We approach the problem through the lens of kernel-based two-sample testing and introduce a sequential testing procedure based on random Fourier features, running with logarithmic time complexity per observation and with overall logarithmic space complexity. The algorithm has two advantages compared to the state of the art. First, our approach is genuinely online, and no access to training data known to be from the pre-change distribution is necessary. Second, the algorithm does not require the user to specify a window parameter over which local tests are to be calculated. We prove strong theoretical guarantees on the algorithm's performance, including information-theoretic bounds demonstrating that the detection delay is optimal in the minimax sense. Numerical studies on real and synthetic data show that our algorithm is competitive with respect to the state of the art.