Statistical Quantification of Differential Privacy: A Local Approach

TL;DR

This paper proposes a new local statistical method for quantifying differential privacy in black box algorithms, providing estimators and confidence intervals that are easy to implement and validated through experiments.

Contribution

Introduces a local characterization-based approach for statistical quantification of differential privacy, avoiding event selection and enabling practical privacy validation.

Findings

Fast convergence rates of estimators

Asymptotic validity of confidence intervals

Experimental confirmation of method efficacy

Abstract

In this work, we introduce a new approach for statistical quantification of differential privacy in a black box setting. We present estimators and confidence intervals for the optimal privacy parameter of a randomized algorithm $A$, as well as other key variables (such as the "data-centric privacy level"). Our estimators are based on a local characterization of privacy and in contrast to the related literature avoid the process of "event selection" - a major obstacle to privacy validation. This makes our methods easy to implement and user-friendly. We show fast convergence rates of the estimators and asymptotic validity of the confidence intervals. An experimental study of various algorithms confirms the efficacy of our approach.