Sequential Change Detection for Multiple Data Streams with Differential Privacy

• URL: http://arxiv.org/abs/2604.13274v1
• Date: Tue, 14 Apr 2026 20:08:07 GMT
• Title: Sequential Change Detection for Multiple Data Streams with Differential Privacy
• Abstract summary: We study sequential change-point detection for multiple data streams under differential privacy constraints.<n>We propose DP-SUM-CUSUM, a differentially private detection procedure based on the summation of per-stream CUSUM statistics with calibrated Laplace noise injection.<n>We show that DP-SUM-CUSUM satisfies sequential $varepsilon$-differential privacy and derive bounds on the average run length to false alarm and the worst-case average detection delay.
• Score: 9.023577624579078
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sequential change-point detection seeks to rapidly identify distributional changes in streaming data while controlling false alarms. Existing multi-stream detection methods typically rely on non-private access to raw observations or intermediate statistics, limiting their usage in privacy-sensitive settings. We study sequential change-point detection for multiple data streams under differential privacy constraints. We consider multiple independent streams undergoing a synchronized change at an unknown time and in an unknown subset of streams, and propose DP-SUM-CUSUM, a differentially private detection procedure based on the summation of per-stream CUSUM statistics with calibrated Laplace noise injection. We show that DP-SUM-CUSUM satisfies sequential $\varepsilon$-differential privacy and derive bounds on the average run length to false alarm and the worst-case average detection delay, explicitly characterizing the privacy--efficiency tradeoff. A truncation-based extension is also presented to handle distributional shifts with unbounded log-likelihood ratios. Simulations and experiments on an Internet of Things (IoT) botnet dataset validate the proposed approach.

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