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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.18562 |
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| _version_ | 1866908871023394816 |
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| author | Lee, Jonghyeok Xie, Yao Park, Youngser Hindes, Jason Schwartz, Ira Priebe, Carey |
| author_facet | Lee, Jonghyeok Xie, Yao Park, Youngser Hindes, Jason Schwartz, Ira Priebe, Carey |
| contents | 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 performance by characterizing the expected detection delay (EDD) under a prescribed average run length (ARL), deriving closed-form asymptotically optimal choices of the window size and drift. We further prove that MRS-C is first-order asymptotically optimal relative to the oracle Exact CUSUM, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we use a parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-Rank Subspace Change-Point Detection for Monitoring Robotic Swarms Lee, Jonghyeok Xie, Yao Park, Youngser Hindes, Jason Schwartz, Ira Priebe, Carey Methodology 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 performance by characterizing the expected detection delay (EDD) under a prescribed average run length (ARL), deriving closed-form asymptotically optimal choices of the window size and drift. We further prove that MRS-C is first-order asymptotically optimal relative to the oracle Exact CUSUM, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we use a parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness. |
| title | Multi-Rank Subspace Change-Point Detection for Monitoring Robotic Swarms |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.18562 |