Year: 2025
Type: preprint
Abstract: We study real-time detection of low-rank changes in the covariance structure of high-dimensional streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we propose the Multi-rank Subspace-CUSUM (MRS-C) procedure, which extends classical CUSUM by tracking projection energy onto an estimated signal subspace. We analyze the immediate-change expected detection delay (EDD), deriving closed-form choices of the window size and drift parameter that minimize the leading-order asymptotic EDD approximation. We further establish an oracle-relative asymptotic efficiency result, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we propose a practical parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness.
Source: arXiv (Cornell University)
Authors: Lee, Jonghyeok, Xie, Yao, Park, Youngser, Hindes, Jason, Schwartz, Ira, Priebe, Carey
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Funder: Office of Naval Research
Award: G6511375413
OpenAlex ID: W6979319395
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