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

Change Detection with the Kernel Cumulative Sum Algorithm