  We present a new non-parametric statistic, called the weighed $\ell_2$
divergence, based on empirical distributions for sequential change detection.
We start by constructing the weighed $\ell_2$ divergence 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 weighed
$\ell_2$ divergence 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.
