Sequential Change Detection by Optimal Weighted ℓ_2 Divergence
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We present a new non-parametric statistics, called the weighted ℓ_2 divergence, based on empirical distributions for sequential change detection. We start by constructing the weighted ℓ_2 divergence as a fundamental building block of sequential 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 weighted ℓ_2 divergence and characterize the fundamental performance metrics, including the Average Run Length (ARL) and the Expected Detection Delay (EDD). We also present practical optimization projection algorithms to handle high-dimensional data, which is critical to quick detection: in such settings, one does not have 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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