Efficient and Private Marginal Reconstruction with Local Non-Negativity

TL;DR

This paper presents ReM and GReM-LNN, new methods for reconstructing marginal query answers under differential privacy, improving accuracy and efficiency in high-dimensional private data analysis.

Contribution

The paper introduces ReM and GReM-LNN, novel postprocessing algorithms that enhance private marginal query reconstruction with efficiency and non-negativity constraints.

Findings

ReM improves accuracy of marginal query reconstruction.

GReM-LNN reduces error using Gaussian noise with non-negativity.

Methods enhance existing private query mechanisms.

Abstract

Differential privacy is the dominant standard for formal and quantifiable privacy and has been used in major deployments that impact millions of people. Many differentially private algorithms for query release and synthetic data contain steps that reconstruct answers to queries from answers to other queries that have been measured privately. Reconstruction is an important subproblem for such mechanisms to economize the privacy budget, minimize error on reconstructed answers, and allow for scalability to high-dimensional datasets. In this paper, we introduce a principled and efficient postprocessing method ReM (Residuals-to-Marginals) for reconstructing answers to marginal queries. Our method builds on recent work on efficient mechanisms for marginal query release, based on making measurements using a residual query basis that admits efficient pseudoinversion, which is an important primitive used in reconstruction. An extension GReM-LNN (Gaussian Residuals-to-Marginals with Local Non-negativity) reconstructs marginals under Gaussian noise satisfying consistency and non-negativity, which often reduces error on reconstructed answers. We demonstrate the utility of ReM and GReM-LNN by applying them to improve existing private query answering mechanisms.