Online Change-Point Detection in RKHS: A Non-Asymptotic Performance Analysis

We study online change-point detection based on the empirical regularized Pearson divergence in a reproducing kernel Hilbert space (RKHS). The proposed procedure compares a left reference window, representing the nominal regime, with a right test window, containing the most recent observations. Although the resulting sliding-window statistic admits a tractable closed-form expression, the main contribution of this paper is a non-asymptotic analysis of its sequential detection performance. Under a bounded-kernel assumption, we derive finite-sample concentration inequalities under the null and obtain explicit threshold calibrations guaranteeing either average-run length control or uniform false-alarm control over an infinite horizon. Under the alternative, we establish non-asymptotic bounds on the per time miss-detection probability and on the tail of the detection delay. The analysis highlights the roles of partial contamination of the test window, regularization, and the window lengths. Experiments support the theoretical findings.