Model-Free Change Point Detection for Mixing Processes

Abstract

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 $\varphi$-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 $\varphi$-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.

20 pages, 4 figures. Accepted by IEEE OJ-CSYS

References in corpus (12)

• Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions
• Kernel Mean Embedding of Distributions: A Review and Beyond
• Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks
• Hilbert space embeddings and metrics on probability measures
• Concentration inequalities for dependent Random variables via the martingale method
• On Optimality Properties of the Shiryaev-Roberts Procedure
• Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence
• MMD Aggregated Two-Sample Test
• Change Detection of Markov Kernels with Unknown Pre and Post Change Kernel
• Efficient Aggregated Kernel Tests using Incomplete $U$-statistics
• MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting
• Spectral Regularized Kernel Two-Sample Tests