Optimal Sub-sampling to Boost Power of Kernel Sequential Change-point Detection

Abstract

We present a novel scheme to boost detection power for kernel maximum mean discrepancy based sequential change-point detection procedures. Our proposed scheme features an optimal sub-sampling of the history data before the detection procedure, in order to tackle the power loss incurred by the random sub-sample from the enormous history data. We apply our proposed scheme to both Scan $B$ and Kernel Cumulative Sum (CUSUM) procedures, and improved performance is observed from extensive numerical experiments.