Marginal Release Under Local Differential Privacy

TL;DR

This paper introduces algorithms for accurately releasing marginal statistics under local differential privacy, with theoretical bounds and empirical validation showing Fourier-based methods outperform direct marginal approaches.

Contribution

It provides the first tight theoretical bounds and empirical evaluation for local differential privacy algorithms for marginal statistics, highlighting the effectiveness of Fourier-based techniques.

Findings

Fourier-based methods outperform direct marginal approaches.

Theoretical bounds on accuracy are established and validated.

Algorithms enable privacy-preserving analysis of multidimensional data.

Abstract

Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding correlations in the data to fitting sophisticated prediction models. In this paper, we provide a set of algorithms for materializing marginal statistics under the strong model of local differential privacy. We prove the first tight theoretical bounds on the accuracy of marginals compiled under each approach, perform empirical evaluation to confirm these bounds, and evaluate them for tasks such as modeling and correlation testing. Our results show that releasing information based on (local) Fourier transformations of the input is preferable to alternatives based directly on (local) marginals.