Relaxed Marginal Consistency for Differentially Private Query Answering

TL;DR

This paper introduces a relaxed marginal consistency method for differentially private query answering that enhances scalability and accuracy without increasing privacy costs by relaxing constraints in the data distribution estimation process.

Contribution

It proposes a novel relaxation of consistency constraints in private data distribution estimation, improving scalability and accuracy of private query answering methods.

Findings

Improves scalability of private query answering in high dimensions.

Enhances accuracy of query responses without additional privacy loss.

Compatible with existing private query algorithms.

Abstract

Many differentially private algorithms for answering database queries involve a step that reconstructs a discrete data distribution from noisy measurements. This provides consistent query answers and reduces error, but often requires space that grows exponentially with dimension. Private-PGM is a recent approach that uses graphical models to represent the data distribution, with complexity proportional to that of exact marginal inference in a graphical model with structure determined by the co-occurrence of variables in the noisy measurements. Private-PGM is highly scalable for sparse measurements, but may fail to run in high dimensions with dense measurements. We overcome the main scalability limitation of Private-PGM through a principled approach that relaxes consistency constraints in the estimation objective. Our new approach works with many existing private query answering algorithms and improves scalability or accuracy with no privacy cost.