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This paper introduces DP-SUM-CUSUM, a differentially private algorithm for detecting synchronized change points across multiple data streams. The method aggregates differentially private CUSUM statistics from each stream using Laplace noise injection to ensure overall privacy. Theoretical analysis provides bounds on false alarm rates and detection delay, explicitly quantifying the privacy-efficiency tradeoff, and the approach is validated on an IoT botnet dataset.
Guaranteeing privacy in multi-stream change detection doesn't have to sacrifice detection speed, as demonstrated by a new algorithm with provable privacy-efficiency tradeoffs.
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.