Model-Free Change Point Detection for Mixing Processes
CoRR(2023)
摘要
This paper considers the change point detection problem under dependent
samples. In particular, we provide performance guarantees for the MMD-CUSUM
test under $\alpha$, $\beta$, and $\phi$-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 $\phi$-mixing processes. The MMD-CUSUM test also achieves strong
performance under $\alpha$/$\beta$-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.
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关键词
Change point detection,kernel method,mixing processes
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