Accuracy for Differentially Private Quotients by Fractional Uncertainties

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.