Model-Free Change Point Detection for Mixing Processes
| Autor: | Chen, Hao, Gupta, Abhishek, Sun, Yin, Shroff, Ness |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/OJCSYS.2024.3398530 |
| Popis: | 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. Comment: 20 pages, 4 figures. Accepted by IEEE OJ-CSYS |
| Databáze: | arXiv |
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