Sequential Change Detection for Multiple Data Streams with Differential Privacy

2026-04-14

AI Summary

This work addresses the problem of detecting simultaneous distributional shifts occurring in an unknown subset of multiple data streams. It introduces differential privacy into multi-stream sequential change-point detection for the first time, proposing the DP-SUM-CUSUM algorithm. The method aggregates CUSUM statistics from individual streams with calibrated noise to achieve ε-differential privacy along the sequence while maintaining high detection efficiency. A truncation mechanism is incorporated to handle unbounded log-likelihood ratios. Theoretical analysis establishes bounds on both the average run length and the worst-case average detection delay, precisely characterizing the trade-off between privacy preservation and detection performance. Empirical evaluation on an IoT botnet dataset demonstrates the effectiveness of the proposed approach.

Technology Category

• Data Mining & Knowledge Management: Data Stream Mining
• Machine Learning: Time-Series/Data Streams
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• sequential change detection
• multiple data streams
• differential privacy
• change-point detection
• privacy-preserving

Innovation

• differential privacy
• sequential change detection
• multi-stream CUSUM
• privacy-efficiency tradeoff
• Laplace noise injection