  This paper considers the change point detection problem under dependent
samples. In particular, we provide performance guarantees for the MMD-CUSUM
test under exponentially $\alpha$, $\beta$, and fast $\phi$-mixing processes,
which significantly expands its utility beyond the i.i.d. and Markovian cases
used in previous studies. We obtain lower bounds for average-run-length (ARL)
and upper bounds for average-detection-delay (ADD) in terms of the threshold
parameter. We show that the MMD-CUSUM test enjoys the same level of performance
as the i.i.d. case under fast $\phi$-mixing processes. The MMD-CUSUM test also
achieves strong performance under exponentially $\alpha$/$\beta$-mixing
processes, which are significantly more relaxed than existing results. The
MMD-CUSUM test statistic adapts to different settings without modifications,
rendering it a completely data-driven, dependence-agnostic change point
detection scheme. Numerical simulations are provided at the end to evaluate our
findings.
