Context-aware Privacy Bounds for Linear Queries

TL;DR

This paper introduces a context-aware privacy analysis for linear queries under differential privacy, leveraging prior distribution assumptions to tighten privacy bounds and reduce noise.

Contribution

It develops a tight, prior-informed leakage bound for linear queries that improves over standard differential privacy guarantees.

Findings

The new bound is strictly tighter than standard DP guarantees.

Exploiting prior knowledge reduces the necessary noise scale.

The bound converges to DP as the prior probability approaches zero.

Abstract

Linear queries, as the basis of broad analysis tasks, are often released through privacy mechanisms based on differential privacy (DP), the most popular framework for privacy protection. However, DP adopts a context-free definition that operates independently of the data-generating distribution. In this paper, we revisit the privacy analysis of the Laplace mechanism through the lens of pointwise maximal leakage (PML). We demonstrate that the distribution-agnostic definition of the DP framework often mandates excessive noise. To address this, we incorporate an assumption about the prior distribution by lower-bounding the probability of any single record belonging to any specific class. With this assumption, we derive a tight, context-aware leakage bound for general linear queries, and prove that our derived bound is strictly tighter than the standard DP guarantee and converges to the DP guarantee as this probability lower bound approaches zero. Numerical evaluations demonstrate that by exploiting this prior knowledge, the required noise scale can be reduced while maintaining privacy guarantees.