Accuracy for Differentially Private Quotients by Fractional Uncertainties

Paper in proceeding, 2025

Differential Privacy (DP) is a cornerstone for ensuring privacy in
data analysis by injecting carefully calibrated noise into statistical
queries. While numerous DP tools focus on privacy protection,
few provide accuracy information, specially for data-dependent
computations like averages or quotients of DP-sums. This paper
introduces a novel approach to compute confidence intervals, i.e.,
𝛼-𝛽 accuracy, for these computations, leveraging principles from
uncertainty propagation. Our method identifies conditions under
which analytical error can be predicted, revealing two key invariants:
the analytical error improves with large dataset sizes, and
addition of values with higher variability require larger dataset
sizes for accurate estimation. To simplify adoption, we also propose
accuracy tuners to enable rapid determination of minimum
dataset sizes and explore trade-offs between privacy budgets and
the possibility to perform accuracy estimations. Our theoretical
contributions are validated through an empirical evaluation that
explores the applicability of fractional uncertainties for computing
concrete 𝛼-𝛽 error across diverse scenarios.