On Differentially Private Counting on Trees

TL;DR

This paper investigates differentially private counting on hierarchical trees, introducing a new error measure, analyzing existing mechanisms, and proposing improved algorithms for both pure and approximate differential privacy settings.

Contribution

It introduces a novel error measure for DP counting on trees, proves optimality of known mechanisms in pure-DP, and develops new algorithms with better performance in approximate-DP.

Findings

Optimality of known mechanisms under the new error measure in pure-DP

New algorithms significantly improve accuracy in approximate-DP

Enhanced understanding of privacy-utility trade-offs in hierarchical counting

Abstract

We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. Motivated by applications, we propose a new error measure for this problem by considering a combination of multiplicative and additive approximation to the query results. We examine known mechanisms in differential privacy (DP) and prove their optimality, under this measure, in the pure-DP setting. In the approximate-DP setting, we design new algorithms achieving significant improvements over known ones.