Compressive Mechanism: Utilizing Sparse Representation in Differential Privacy

TL;DR

This paper introduces the compressive mechanism, leveraging compressive sensing to significantly reduce noise in differential privacy, improving accuracy for statistical query releases and continual data release scenarios.

Contribution

It presents a novel differential privacy mechanism based on compressive sensing, reducing noise from O(√n) to O(log n) and enabling more accurate data releases.

Findings

Noise reduced from O(√n) to O(log n)

Effective for continual statistical data release

Validated with real datasets

Abstract

Differential privacy provides the first theoretical foundation with provable privacy guarantee against adversaries with arbitrary prior knowledge. The main idea to achieve differential privacy is to inject random noise into statistical query results. Besides correctness, the most important goal in the design of a differentially private mechanism is to reduce the effect of random noise, ensuring that the noisy results can still be useful. This paper proposes the \emph{compressive mechanism}, a novel solution on the basis of state-of-the-art compression technique, called \emph{compressive sensing}. Compressive sensing is a decent theoretical tool for compact synopsis construction, using random projections. In this paper, we show that the amount of noise is significantly reduced from $O(\sqrt{n})$ to $O(\log(n))$, when the noise insertion procedure is carried on the synopsis samples instead of the original database. As an extension, we also apply the proposed compressive mechanism to solve the problem of continual release of statistical results. Extensive experiments using real datasets justify our accuracy claims.