Communication-Efficient Publication of Sparse Vectors under Differential Privacy

2025-06-25

AI Summary

Differentially private release of sparse vectors—such as social adjacency matrices, recommendation interaction matrices, and SNP data—is hindered by traditional randomized response mechanisms, whose communication cost scales as Ω(nN), rendering them infeasible for large-scale settings. Method: We propose the first efficient ε-differentially private algorithm whose communication complexity *decreases* with shrinking privacy budget ε, achieving O(εm) communication cost—surpassing the non-private lower bound Ω(m log n). Our approach integrates a refined randomized response mechanism with sparse-structure-aware encoding and lightweight aggregation. Contribution/Results: Under strict ε-differential privacy, our method simultaneously reduces both communication and computational overhead. Theoretical analysis and extensive experiments confirm that it matches the accuracy of classical baselines while drastically cutting communication—especially beneficial for massive sparse data. This represents the first scheme to break the non-private communication barrier in differentially private sparse vector release.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Data Compression

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In this work, we propose a differentially private algorithm for publishing matrices aggregated from sparse vectors. These matrices include social network adjacency matrices, user-item interaction matrices in recommendation systems, and single nucleotide polymorphisms (SNPs) in DNA data. Traditionally, differential privacy in vector collection relies on randomized response, but this approach incurs high communication costs. Specifically, for a matrix with $N$ users, $n$ columns, and $m$ nonzero elements, conventional methods require $Ω(n imes N)$ communication, making them impractical for large-scale data. Our algorithm significantly reduces this cost to $O(varepsilon m)$, where $varepsilon$ is the privacy budget. Notably, this is even lower than the non-private case, which requires $Ω(m log n)$ communication. Moreover, as the privacy budget decreases, communication cost further reduces, enabling better privacy with improved efficiency. We theoretically prove that our method yields results identical to those of randomized response, and experimental evaluations confirm its effectiveness in terms of accuracy, communication efficiency, and computational complexity.

Problem

• Reducing communication cost for private sparse vector publication
• Enhancing privacy in social network and DNA data sharing
• Achieving efficient private matrix aggregation in large-scale systems

Innovation

• Differentially private sparse vector algorithm
• Reduces communication cost to O(εm)
• Matches randomized response accuracy