Information-Theoretic Privacy-Preserving Schemes Based On Perfect Privacy

TL;DR

This paper explores information-theoretic privacy schemes that balance data utility and privacy by maximizing disclosed information about a variable while limiting leakage about another, using mutual information as a measure.

Contribution

It introduces privacy-preserving schemes based on generalized independence, provides closed-form solutions in specific cases, and analyzes the utility-privacy trade-off's convexity.

Findings

Proposed privacy schemes generalize statistical independence.

Derived closed-form solutions for specific scenarios.

Analyzed convexity of utility-privacy trade-off functions.

Abstract

Consider a pair of random variables $(X,Y)$ distributed according to a given joint distribution $p_{XY}$. A curator wishes to maximally disclose information about $Y$, while limiting the information leakage incurred on $X$. Adopting mutual information to measure both utility and privacy of this information disclosure, the problem is to maximize $I(Y;U)$, subject to $I(X;U)\leq\epsilon$, where $U$ denotes the released random variable and $\epsilon$ is a given privacy threshold. Two settings are considered, where in the first one, the curator has access to $(X,Y)$, and hence, the optimization is over $p_{U|XY}$, while in the second one, the curator can only observe $Y$ and the optimization is over $p_{U|Y}$. In both settings, the utility-privacy trade-off is investigated from theoretical and practical perspective. More specifically, several privacy-preserving schemes are proposed in these settings based on generalizing the notion of statistical independence. Moreover, closed-form solutions are provided in certain scenarios. Finally, convexity arguments are provided for the utility-privacy trade-off as functionals of the joint distribution $p_{XY}$.