Kernel QuantTree

We present Kernel QuantTree (KQT), a non-parametric change detection algorithm that monitors multivariate data through a histogram. KQT constructs a nonlinear partition of the input space that matches pre-defined target probabilities and specifically promotes compact bins adhering to the data distribution, resulting in a powerful detection algorithm. We prove two key theoretical advantages of KQT: i) statistics defined over the KQT histogram do not depend on the stationary data distribution $\phi_0$, so detection thresholds can be set a priori to control false positive rate, and ii) thanks to the kernel functions adopted, the KQT monitoring scheme is invariant to the roto-translation of the input data. Consequently, KQT does not require any preprocessing step like PCA. Our experiments show that KQT achieves superior detection power than non-parametric state-of-the-art change detection methods, and can reliably control the false positive rate.