Skirting Additive Error Barriers for Private Turnstile Streams

2026-02-10

AI Summary

This work addresses the challenge of continuously releasing statistics over turnstile streams under differential privacy, where existing methods are constrained by an Ω(T^{1/4}) lower bound on additive error for problems such as distinct count and F₂ estimation. To overcome this barrier, we introduce a novel hybrid additive-multiplicative error model and present the first private streaming algorithms that achieve polylog(T) additive error alongside (1+o(1)) multiplicative error, all within polylog(T) space. By integrating multi-scale sampling, sparse vector techniques, and careful streaming algorithm design, our approach significantly improves upon prior solutions that required polynomial space and incurred polynomial additive error, thereby enabling efficient and accurate private continuous release for fundamental stream statistics.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Data Stream Mining

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We study differentially private continual release of the number of distinct items in a turnstile stream, where items may be both inserted and deleted. A recent work of Jain, Kalemaj, Raskhodnikova, Sivakumar, and Smith (NeurIPS'23) shows that for streams of length $T$, polynomial additive error of $\Omega(T^{1/4})$ is necessary, even without any space restrictions. We show that this additive error lower bound can be circumvented if the algorithm is allowed to output estimates with both additive \emph{and multiplicative} error. We give an algorithm for the continual release of the number of distinct elements with $\text{polylog} (T)$ multiplicative and $\text{polylog}(T)$ additive error. We also show a qualitatively similar phenomenon for estimating the $F_2$ moment of a turnstile stream, where we can obtain $1+o(1)$ multiplicative and $\text{polylog} (T)$ additive error. Both results can be achieved using polylogarithmic space whereas prior approaches use polynomial space. In the sublinear space regime, some multiplicative error is necessary even if privacy is not a consideration. We raise several open questions aimed at better understanding trade-offs between multiplicative and additive error in private continual release.

Problem

• differential privacy
• turnstile streams
• additive error
• multiplicative error
• continual release

Innovation

• differential privacy
• continual release
• turnstile streams
• multiplicative error
• sublinear space