A nonparametric information theoretic approach for change detection in time series

This paper presents an online nonparametric methodology based on the Kernel Least Mean Square (KLMS) algorithm and the surprise criterion, which is based on an information theoretic framework. Surprise quantifies the amount of information a datum contains given a known system state, and can be estimated online using Gaussian Process Theory. Based on this concept, we use the KLMS algorithm together with surprise criterion to detect regime change in nonstationary time series. We test the methodology on a synthesized chaotic time series to illustrate this criterion. The results show that surprise criterion is better than the conventional segmentation based on the error criterion.