New Privacy Mechanism Design With Direct Access to the Private Data

TL;DR

This paper introduces a new privacy mechanism that allows direct access to private data, improving privacy-utility trade-offs by deriving tighter bounds and employing novel theoretical tools.

Contribution

It proposes a new privacy mechanism design using extended functional representation lemmas and a separation technique, advancing the theoretical bounds on privacy-utility trade-offs.

Findings

Derived new lower bounds on privacy-utility trade-off.

Showed bounds can outperform previous results.

Analyzed bounds in various scenarios.

Abstract

The design of a statistical signal processing privacy problem is studied where the private data is assumed to be observable. In this work, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A statistical privacy mechanism is employed to generate data $U$ based on $(X,Y)$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. To this end, we use extended versions of the Functional Representation Lemma and Strong Functional Representation Lemma and combine them with a simple observation which we call separation technique. New lower bounds on privacy-utility trade-off are derived and we show that they can improve the previous bounds. We study the obtained bounds in different scenarios and compare them with previous results.