A Theoretical and Empirical Examination of Differential Privacy Mechanisms in High-Dimensional Data Environments for Public Sector Analytics

Abstract

The integration of differential privacy (DP) mechanisms into public sector analytics has become increasingly critical in the era of high-dimensional data, where privacy preservation and analytical utility are often at odds. This paper provides a focused theoretical and empirical investigation of the effectiveness of prominent DP algorithms—particularly the Laplace and Gaussian mechanisms—within high-dimensional public datasets. We evaluate the performance trade-offs across varying privacy budgets and dimensionalities, using real-world census and health datasets. Our findings highlight that while noise calibration in high-dimensional settings preserves privacy, it often leads to significant utility degradation, necessitating smarter dimensionality reduction and adaptive noise distribution.