Correlated-Sequence Differential Privacy

TL;DR

This work tackles privacy for correlated sequential data by introducing Correlated-Sequence Differential Privacy (CSDP) and modeling multivariate streams as Coupling Markov Chains (CMC). It derives both loose and tight leakage bounds based on spectral properties, revealing that stronger coupling can disperse perturbations and reduce worst-case leakage. The Freshness-Regulated Adaptive Noise (FRAN) mechanism combines data aging and correlation-aware Laplace noise to achieve a linear-time release while preserving utility. Empirical results on two-sequence datasets show that CSDP improves the privacy-utility trade-off by about 50% over existing correlated-DP methods and by roughly two orders of magnitude over standard DP, indicating strong practical potential for privacy-preserving analytics in healthcare, finance, and IoT contexts.

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.

Figures (5)

• Figure 1: An illustration of CMC model.
• Figure 2: The illustration of FRAN mechanism for CSDP.
• Figure 3: Privacy leakage level v.s. different parameters. We set $p = q = 0.3$ and $\lambda = \lambda_{11} = \lambda_{22}$ across all experiments.
• Figure 4: Comprehensive analysis of privacy-utility trade-offs in CSDP framework. We set $p = q = 0.3$ and $\lambda = 0.75$ across all experiments.
• Figure 5: Minimum privacy leakage level vs. accuracy constraint for different privacy mechanisms.

Theorems & Definitions (19)

• Definition 1: DP dwork2006differential
• Definition 2: $\ell_1$-Sensitivity
• Definition 3: Laplace Mechanism
• Definition 4: ADP Zhang2023
• Definition 5: Neighbouring spatio-temporal databases
• Definition 6: CSDP
• proof : Proof Sketch
• Definition 7: Correlation degree $k$
• Definition 8: $k$-sensitivity $d(k)$
• Definition 9: Aged correlation distance $\Delta_{k}$