{"ID":2875611,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.02768","arxiv_id":"2509.02768","title":"Sequential Change Detection with Differential Privacy","abstract":"Sequential change detection is a fundamental problem in statistics and signal processing, with the CUSUM procedure widely used to achieve minimax detection delay under a prescribed false-alarm rate when pre- and post-change distributions are fully known. However, releasing CUSUM statistics and the corresponding stopping time directly can compromise individual data privacy. We therefore introduce a differentially private (DP) variant, called DP-CUSUM, that injects calibrated Laplace noise into both the vanilla CUSUM statistics and the detection threshold, preserving the recursive simplicity of the classical CUSUM statistics while ensuring per-sample differential privacy. We derive closed-form bounds on the average run length to false alarm and on the worst-case average detection delay, explicitly characterizing the trade-off among privacy level, false-alarm rate, and detection efficiency. Our theoretical results imply that under a weak privacy constraint, our proposed DP-CUSUM procedure achieves the same first-order asymptotic optimality as the classical, non-private CUSUM procedure. Numerical simulations are conducted to demonstrate the detection efficiency of our proposed DP-CUSUM under different privacy constraints, and the results are consistent with our theoretical findings.","short_abstract":"Sequential change detection is a fundamental problem in statistics and signal processing, with the CUSUM procedure widely used to achieve minimax detection delay under a prescribed false-alarm rate when pre- and post-change distributions are fully known. However, releasing CUSUM statistics and the corresponding stoppin...","url_abs":"https://arxiv.org/abs/2509.02768","url_pdf":"https://arxiv.org/pdf/2509.02768v2","authors":"[\"Liyan Xie\",\"Ruizhi Zhang\"]","published":"2025-09-02T19:15:47Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}