The Utility Cost of Robust Privacy Guarantees

Abstract

Consider a data publishing setting for a data set with public and private features. The objective of the publisher is to maximize the amount of information about the public features in a revealed data set, while keeping the information leaked about the private features bounded. The goal of this paper is to analyze the performance of privacy mechanisms that are constructed to match the distribution learned from the data set. Two distinct scenarios are considered: (i) mechanisms are designed to provide a privacy guarantee for the learned distribution; and (ii) mechanisms are designed to provide a privacy guarantee for every distribution in a given neighborhood of the learned distribution. For the first scenario, given any privacy mechanism, upper bounds on the difference between the privacy-utility guarantees for the learned and true distributions are presented. In the second scenario, upper bounds on the reduction in utility incurred by providing a uniform privacy guarantee are developed.

Optimal Utility-Privacy Trade-Off With Total Variation Distance as a Privacy Measure

“…In this regard, [14], [16], [23] propose a training method based on the application of Generative Adversarial Networks (GAN) framework [24], which can be captured as a minimax game between two parties, as a datadriven approach to address this problem. As a related work, [25] analyzes the performance of privacy-preserving release mechanisms under partial knowledge of the input distribution for different privacy measures. It is important to note that the proposed privacy measure, i.e., T (•; •) guarantees pointwise and uniform privacy according to [25,Theorems 1,2].…”

“…As a related work, [25] analyzes the performance of privacy-preserving release mechanisms under partial knowledge of the input distribution for different privacy measures. It is important to note that the proposed privacy measure, i.e., T (•; •) guarantees pointwise and uniform privacy according to [25,Theorems 1,2]. An extension of the current work is to address the utility-privacy trade-off under the privacy measure T (X; U ) when only a limited number of observed data samples are available to the release mechanism.…”

Privacy Under Hard Distortion Constraints

“…The feasible ball B D (x) around x is defined in (9). For the distribution independent PUT in (13), we have…”

“…The exact nature of the privacy-utility tradeoff (PUT) will depend to varying degrees on the distribution of the underlying data, as well as the chosen metrics (e.g., differential privacy [1], mutual information (MI) [2], [3], f -divergencebased leakage measures [4], maximal leakage (MaxL) [5]). Furthermore, most information-theoretic PUTs capture utility as a statistical average of desired measures of fidelity [6]- [9]. This, in turn, simplifies the PUT to a single-letter optimization for independent and identically distributed (i.i.d.)…”

A Generalization of the Stratonovich's Value of Information and Application to Privacy-Utility Trade-off

“…Some examples are Arimoto's MI [6], Sibson's MI [7], and Csiszár's MI [8]. Recently, new information leakage measures have been proposed in the privacy-utility trade-off (PUT) problem, such as finformation [9] and f -leakage [10], as privacy measures. In addition to these measures, by assuming a "guessing" adversary, information leakage measures that have operational meanings have been proposed.…”