Low Rank Mechanism for Optimizing Batch Queries under Differential Privacy

TL;DR

This paper introduces the Low-Rank Mechanism (LRM), a practical approach that uses low-rank approximation to improve the accuracy of batch query answers under differential privacy, outperforming existing methods.

Contribution

The paper presents the first practical differentially private method for batch queries based on low-rank approximation, achieving near-optimal accuracy and outperforming state-of-the-art solutions.

Findings

LRM significantly improves query accuracy over existing methods.

LRM's accuracy is close to the theoretical lower bound.

Extensive experiments validate LRM's superior performance.

Abstract

Differential privacy is a promising privacy-preserving paradigm for statistical query processing over sensitive data. It works by injecting random noise into each query result, such that it is provably hard for the adversary to infer the presence or absence of any individual record from the published noisy results. The main objective in differentially private query processing is to maximize the accuracy of the query results, while satisfying the privacy guarantees. Previous work, notably \cite{LHR+10}, has suggested that with an appropriate strategy, processing a batch of correlated queries as a whole achieves considerably higher accuracy than answering them individually. However, to our knowledge there is currently no practical solution to find such a strategy for an arbitrary query batch; existing methods either return strategies of poor quality (often worse than naive methods) or require prohibitively expensive computations for even moderately large domains. Motivated by this, we propose the \emph{Low-Rank Mechanism} (LRM), the first practical differentially private technique for answering batch queries with high accuracy, based on a \emph{low rank approximation} of the workload matrix. We prove that the accuracy provided by LRM is close to the theoretical lower bound for any mechanism to answer a batch of queries under differential privacy. Extensive experiments using real data demonstrate that LRM consistently outperforms state-of-the-art query processing solutions under differential privacy, by large margins.