Change Detection with the Kernel Cumulative Sum Algorithm

Online change detection involves monitoring a stream of data for changes in the statistical properties of incoming observations. A good change detector will detect any changes shortly after they occur, while raising few false alarms. Although there are algorithms with confirmed optimality properties for this task, they rely on the exact specifications of the relevant probability distributions and this limits their practicality. In this work we describe a kernel-based variant of the Cumulative Sum (CUSUM) change detection algorithm that can detect changes under less restrictive assumptions. Instead of using the likelihood ratio, which is a parametric quantity, the Kernel CUSUM (KCUSUM) algorithm compares incoming data with samples from a reference distribution using a statistic based on the Maximum Mean Discrepancy (MMD) non-parametric testing framework. The KCUSUM algorithm is applicable in settings where there is a large amount of background data available and it is desirable to detect a change away from this background setting. Exploiting the random-walk structure of the test statistic, we derive bounds on the performance of the algorithm, including the expected delay and the average time to false alarm.