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

TL;DR

This paper introduces KQT-EWMA, a non-parametric, online change detection method for multivariate data streams that effectively controls false alarms and detects changes with low delay, regardless of the underlying data distribution.

Contribution

The paper proposes KQT-EWMA, a novel non-parametric change detection algorithm combining Kernel-QuantTree histograms with EWMA, capable of controlling false alarm rates in online multivariate data monitoring.

Findings

KQT-EWMA effectively controls the ARL_0 parameter.

It achieves detection delays comparable or lower than existing methods.

Demonstrated on synthetic and real-world datasets.

Abstract

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.