Edit-Neighboring Data Streams and Privacy under Continual Observation

2026-07-22

AI Summary

This work addresses the privacy leakage arising from temporal shifts in data streams caused by individual participation under continuous observation. To model this more stringent dynamic privacy setting, the paper introduces, for the first time, the “edit-adjacent data stream” framework. Within this model, the authors design the first differentially private mechanism achieving polylogarithmic additive error and establish a fundamental lower bound of Ω̃(min{T^{1/3}/ε^{2/3}, T}) on the error of any additive-noise mechanism. Their mechanism matches the error rate of standard settings while offering a superior trade-off between generality and accuracy. Empirical evaluations demonstrate that it achieves a better balance between attack success rate and utility loss compared to existing approaches.

Abstract

Differential privacy under Continual Observation (CO) quantifies the loss in privacy that occurs when outputs generated using a stream of sensitive input data are published in the online setting. In this paper, we consider a more stringent notion of privacy compared to prior work wherein an individual's participation may shift the entire stream by a time-step. We define a new notion of edit-neighboring streams that captures this scenario. Our findings are as follows. First, we prove that on a stream of length $T$, every additive-noise mechanism incurs error $\tildeΩ(\min\{T^{1/3}/\varepsilon^{2/3}, T\})$ when required to be $\varepsilon$-DP under CO for edit-neighboring streams. This includes state-of-the-art continual counters constructed via the factorization mechanism that in the standard neighboring setting incur only polylogarithmic additive error. Second, we construct the first mechanisms with polylogarithmic additive error for our more stringent notion of privacy. We show that we can recover the same additive error as in the standard notion of privacy albeit with worse constant coefficients for both arbitrary input streams and sparse streams. Third, we show that the notion of edit-neighboring streams inhabits a `sweet-spot' in terms of generality and additive error incurred. More precisely, we show that the even more general notion of prefix-sum neighboring streams---which arises naturally in reductions for problems under CO---must incur additive error scaling as $\tildeΩ(\min\{T^{1/3}/\varepsilon^{2/3}, T\})$ for any mechanism that is $\varepsilon$-DP under continual observation. Finally, we show empirically on synthetic data that when compared with prior work, our mechanism achieves a superior trade-off between the success probability of a simple distinguishing attack, and the additive error incurred by the respective mechanisms.

Problem

• differential privacy
• continual observation
• edit-neighboring streams
• additive error
• data streams

Innovation

• edit-neighboring streams
• continual observation
• differential privacy
• additive error
• factorization mechanism