differentialprivacy

Differential privacy is a mathematical framework for quantifying and protecting the privacy of individuals in datasets from statistical analyses and data releases. It provides guarantees that the inclusion or exclusion of a single individual's data has only a limited effect on the outputs of a data-analysis mechanism.

The core idea is formalized via a randomized mechanism M. In its standard form, M gives epsilon-differential privacy if, for all datasets D and D' that differ in one element, and for all possible outputs S, the probabilities satisfy Pr[M(D) in S] ≤ exp(epsilon) · Pr[M(D') in S]. Epsilon is a nonnegative parameter controlling privacy loss; smaller epsilon yields stronger privacy. A relaxed version, (epsilon, delta)-differential privacy, allows a small probability delta of larger deviations.

Common DP mechanisms add calibrated random noise. The Laplace mechanism adds Laplace noise to numeric query results; the Gaussian mechanism adds Gaussian noise to achieve (epsilon, delta)-DP; the Exponential mechanism selects among outputs with probability proportional to a quality score. Local differential privacy denies that the data is ever revealed in a non-noised form by randomizing data on the user's device before transmission; central DP relies on a trusted curator. Privacy budgets and composition rules describe how privacy loss compounds across multiple analyses.

Applications include private data analysis, statistics, and machine learning. DP has been adopted in national statistics programs and by technology companies; for example, data releases by the US Census Bureau use differential privacy, and industry uses include privacy-preserving machine learning with DP-SGD. Limitations include the trade-off between privacy and utility and the need for careful design to avoid unintended leakage; high-dimensional data and correlated attributes can complicate guarantees.

Differential privacy remains an active area of research, balancing rigorous privacy guarantees with practical utility across domains.