Privacy mechanism design maximizes data utility under bounded leakage
On Privacy Mechanism Design Under a Bounded $α$-Lift Leakage Constraint with $χ^2$-Utility
Information Theory
Summary
This paper looks at how to share useful data while keeping private information safe. The authors focus on a way to measure how much useful information can be kept after privacy protections are applied, using a mathematical measure called Pearson chi-squared information. They provide formulas and mechanisms that guarantee a specific privacy limit is not exceeded while maximizing the usefulness of the released data. Their work also connects to other privacy measures and includes methods that can be computed exactly or approximated with guarantees.
What this means in practice
- •For data privacy engineers: Design privacy-preserving data release mechanisms that maximize utility while rigorously bounding leakage using point-wise constraints.
- •For machine learning deployment teams: Implement privacy-protecting data transformations with explicit guarantees to safely share training or inference data correlated with sensitive attributes.
Authors
Amirreza Zamani, Mohammad Amin Zarrabian, Parastoo Sadeghi, Mikael Skoglund
Abstract
We study the design of a statistical privacy mechanism under a bounded $α$-lift leakage constraint. An agent observes useful data $Y$, which is arbitrarily correlated with private data $X$, and releases $U$. The goal is to maximize Pearson $χ^2$-information $χ^2(Y;U)$ while satisfying the point-wise privacy constraint. This utility is an $f$-information that is nonnegative, obeys data processing, and measures the aggregate normalized change from the prior $P_Y$ to the posteriors $P_{Y|U=u}$. The main benefit of this choice is that $χ^2(Y;U)$ is exactly quadratic in the posterior perturbations; hence, no local approximation of the utility is required. For the nonlinear $α$-lift constraint, we derive a uniform Taylor-remainder bound that remains valid for the optimizing, $ε$-dependent perturbation. When $P_{X|Y}$ is invertible, this yields a closed-form quadratic surrogate, an explicitly scaled binary mechanism that satisfies the original $α$-lift constraint, a computable sufficient range for $ε$, and an $O(ε^{3/2})$ bound on the utility gap. For $α=2$, the solution is exact over an explicit range. We transfer these results to point-wise Rényi-divergence privacy, including an exact-feasible mechanism, an explicit privacy-budget range, and matching gap bounds. We also give an exact formulation for arbitrary leakage matrices and evaluate exact-feasible mechanisms numerically.