Change Detection in Multivariate data streams: Online Analysis with Kernel-QuantTree

We present Kernel-QuantTree Exponentially Weighted Moving Average (KQT-EWMA), a non-parametric change-detection algorithm that combines the Kernel-QuantTree (KQT) histogram and the EWMA statistic to monitor multivariate data streams online. The resulting monitoring scheme is very flexible, since histograms can be used to model any stationary distribution, and practical, since the distribution of test statistics does not depend on the distribution of datastream in stationary conditions (non-parametric monitoring). KQT-EWMA enables controlling false alarms by operating at a pre-determined Average Run Length ($ARL_0$), which measures the expected number of stationary samples to be monitored before triggering a false alarm. The latter peculiarity is in contrast with most non-parametric change-detection tests, which rarely can control the $ARL_0$ a priori. Our experiments on synthetic and real-world datasets demonstrate that KQT-EWMA can control $ARL_0$ while achieving detection delays comparable to or lower than state-of-the-art methods designed to work in the same conditions.

Class Distribution Monitoring for Concept Drift Detection

We introduce Class Distribution Monitoring (CDM), an effective concept-drift detection scheme that monitors the class-conditional distributions of a datastream. In particular, our solution leverages multiple instances of an online and nonparametric change-detection algorithm based on QuantTree. CDM reports a concept drift after detecting a distribution change in any class, thus identifying which classes are affected by the concept drift. This can be precious information for diagnostics and adaptation. Our experiments on synthetic and real-world datastreams show that when the concept drift affects a few classes, CDM outperforms algorithms monitoring the overall data distribution, while achieving similar detection delays when the drift affects all the classes. Moreover, CDM outperforms comparable approaches that monitor the classification error, particularly when the change is not very apparent. Finally, we demonstrate that CDM inherits the properties of the underlying change detector, yielding an effective control over the expected time before a false alarm, or Average Run Length (ARL$_0$).