Flexible Accuracy for Differential Privacy

TL;DR

This paper introduces Flexible Accuracy, a novel approach augmenting differential privacy to handle high-sensitivity functions by allowing small input distortions, enabling new mechanisms for private histograms and extremal data analysis.

Contribution

It proposes a new definitional framework and mechanisms that extend differential privacy to high-sensitivity functions using Flexible Accuracy and lossy Wasserstein distance.

Findings

Mechanisms for differentially private histograms developed.

Extended DP applicability to high-sensitivity functions.

New composition theorems for modular privacy analysis.

Abstract

Differential Privacy (DP) has become a gold standard in privacy-preserving data analysis. While it provides one of the most rigorous notions of privacy, there are many settings where its applicability is limited. Our main contribution is in augmenting differential privacy with {\em Flexible Accuracy}, which allows small distortions in the input (e.g., dropping outliers) before measuring accuracy of the output, allowing one to extend DP mechanisms to high-sensitivity functions. We present mechanisms that can help in achieving this notion for functions that had no meaningful differentially private mechanisms previously. In particular, we illustrate an application to differentially private histograms, which in turn yields mechanisms for revealing the support of a dataset or the extremal values in the data. Analyses of our constructions exploit new versatile composition theorems that facilitate modular design. All the above extensions use our new definitional framework, which is in terms of "lossy Wasserstein distance" -- a 2-parameter error measure for distributions. This may be of independent interest.