Sequential Change Detection by Optimal Weighted ℓ₂ Divergence

Abstract

We present a new non-parametric statistic, called the weighedl2divergence, based on empirical distributions for sequential change detection. We start by constructing the weighedl2divergence as a fundamental building block for two-sample tests and change detection. The proposed statistic is proved to attain the optimal sample complexity in the offline setting. We then study the sequential change detection using the weighedl2divergence and characterize the fundamental performance metrics, including the average run length (ARL) and the expected detection delay (EDD). We also present practical algorithms to find the optimal projection to handle high-dimensional data and the optimal weights, which is critical to quick detection since, in such settings, there are not many post-change samples. Simulation results and real data examples are provided to validate the good performance of the proposed method.

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