Privacy-utility tradeoff with nonspecific tasks: Robust privatization and minimum leakage
Journal
2020 IEEE Information Theory Workshop, ITW 2020
Date Issued
2021
Author(s)
Liu T.-Y
Abstract
Privacy-preserving data release mechanisms aiming to minimize the privacy leakage under utility constraints of nonspecific tasks are studied through the lens of information theory. While the private feature to be protected is typically determined and known by the users who release their data, the specific task where the release data is utilized is usually unknown. To address the lack of information of the specific task, utility constraints laid on a set of multiple possible tasks are considered. The mechanism protects the privacy of a given feature of the to-be-released data while satisfying utility constraints of all possible tasks in the set. First, the single-letter characterization of the privacy-utility tradeoff region is derived. Characterization of the minimum privacy under log-loss utility constraints turns out to be a non-convex optimization problem involving mutual information in the objective function and the constraints. Second, focusing on the case where the raw data consists of multiple independent components, we show that the above optimization problem can be decomposed into multiple parallel privacy funnel (PF) problems [1] with different weightings. We explicitly derive the optimal solution to each PF problem when the private feature is a deterministic function of a data component. The solution is characterized by the leakage-free threshold, and the minimum leakage is zero while the utility constraint is below the threshold. Once the utility requirement is above the threshold, the privacy leakage increases linearly. Finally, we show that the optimal weighting of each privacy funnel problem can be found by solving a linear program (LP). Numerical results are shown to illustrate the robustness of our approach. ?2021 IEEE
Subjects
Convex optimization
Information theory
Linear programming
Privatization
Deterministic functions
Independent components
Mutual informations
Nonconvex optimization
Numerical results
Objective functions
Optimization problems
Privacy preserving
Privacy by design
Type
conference paper