Nonparametric and Online Change Detection in Multivariate Datastreams Using QuantTree

We address the problem of online change detection in multivariate datastreams, and we introduce QuantTree Exponentially Weighted Moving Average (QT-EWMA), a nonparametric change-detection algorithm that can control the expected time before a false alarm, yielding a desired Average Run Length (ARL$_{0}$). Controlling false alarms is crucial in many applications and is rarely guaranteed by online change-detection algorithms that can monitor multivariate datastreams without knowing the data distribution. Like many change-detection algorithms, QT-EWMA builds a model of the data distribution, in our case a QuantTree histogram, from a stationary training set. To monitor datastreams even when the training set is extremely small, we propose QT-EWMA-update, which incrementally updates the QuantTree histogram during monitoring, always keeping the ARL$_{0}$ under control. Our experiments, performed on synthetic and real-world datastreams, demonstrate that QT-EWMA and QT-EWMA-update control the ARL$_{0}$ and the false alarm rate better than state-of-the-art methods operating in similar conditions, achieving lower or comparable detection delays.