Tangent differential privacy
Lexing Ying
TL;DR
The paper introduces tangent differential privacy, a privacy notion that adapts to a target data distribution rather than applying uniformly across all distributions. It develops a tangent-space privacy framework with norm-based bounds using total variation and Wasserstein distances, and shows how entropic regularization yields tangent DP for risk minimization. It provides explicit bounds that depend on the regularization strength and a bound on the risk, along with practical considerations for estimating these quantities. The work points to potential extensions to unsupervised and online learning and discusses sampling-based implementations via Gibbs or Langevin dynamics.
Abstract
Differential privacy is a framework for protecting the identity of individual data points in the decision-making process. In this note, we propose a new form of differential privacy called tangent differential privacy. Compared with the usual differential privacy that is defined uniformly across data distributions, tangent differential privacy is tailored towards a specific data distribution of interest. It also allows for general distribution distances such as total variation distance and Wasserstein distance. In the case of risk minimization, we show that entropic regularization guarantees tangent differential privacy under rather general conditions on the risk function.