Bias and Variance of Post-processing in Differential Privacy

TL;DR

This paper investigates how post-processing affects the bias and variance of differentially private outputs, especially when projecting onto feasible regions, combining theoretical analysis and empirical evaluation.

Contribution

It provides the first detailed analysis of the impact of post-processing on noise distribution in differential privacy, focusing on bias and variance effects.

Findings

Post-processing can introduce bias in private outputs.

Variance may increase or decrease depending on the projection method.

Theoretical and empirical results highlight conditions affecting accuracy.

Abstract

Post-processing immunity is a fundamental property of differential privacy: it enables the application of arbitrary data-independent transformations to the results of differentially private outputs without affecting their privacy guarantees. When query outputs must satisfy domain constraints, post-processing can be used to project the privacy-preserving outputs onto the feasible region. Moreover, when the feasible region is convex, a widely adopted class of post-processing steps is also guaranteed to improve accuracy. Post-processing has been applied successfully in many applications including census data-release, energy systems, and mobility. However, its effects on the noise distribution is poorly understood: It is often argued that post-processing may introduce bias and increase variance. This paper takes a first step towards understanding the properties of post-processing. It considers the release of census data and examines, both theoretically and empirically, the behavior of a widely adopted class of post-processing functions.