Correlated-Sequence Differential Privacy

Abstract

Data streams collected from multiple sources are rarely independent. Values evolve over time and influence one another across sequences. These correlations improve prediction in healthcare, finance, and smart-city control yet violate the record-independence assumption built into most Differential Privacy (DP) mechanisms. To restore rigorous privacy guarantees without sacrificing utility, we introduce Correlated-Sequence Differential Privacy (CSDP), a framework specifically designed for preserving privacy in correlated sequential data. CSDP addresses two linked challenges: quantifying the extra information an attacker gains from joint temporal and cross-sequence links, and adding just enough noise to hide that information while keeping the data useful. We model multivariate streams as a Coupling Markov Chain, yielding the derived loose leakage bound expressed with a few spectral terms and revealing a counterintuitive result: stronger coupling can actually decrease worst-case leakage by dispersing perturbations across sequences. Guided by these bounds, we build the Freshness-Regulated Adaptive Noise (FRAN) mechanism--combining data aging, correlation-aware sensitivity scaling, and Laplace noise--that runs in linear time. Tests on two-sequence datasets show that CSDP improves the privacy-utility trade-off by approximately 50% over existing correlated-DP methods and by two orders of magnitude compared to the standard DP approach.