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This paper considers the change point detection problem under dependentsamples. In particular, we provide performance guarantees for the MMD-CUSUMtest under $\alpha$, $\beta$, and $\phi$-mixing processes, which significantlyexpands its utility beyond the i.i.d. and Markovian cases used in previousstudies. We obtain lower bounds for average-run-length (ARL) and upper boundsfor average-detection-delay (ADD) in terms of the threshold parameter. We showthat the MMD-CUSUM test enjoys the same level of performance as the i.i.d. caseunder $\phi$-mixing processes. The MMD-CUSUM test also achieves strongperformance under $\alpha$/$\beta$-mixing processes, which are significantlymore relaxed than existing results. The MMD-CUSUM test statistic adapts todifferent settings without modifications, rendering it a completelydata-driven, dependence-agnostic change point detection scheme. Numericalsimulations are provided at the end to evaluate our findings.

Model-Free Change Point Detection for Mixing Processes