Achieving Pareto-Optimal MI-Based Privacy-Utility Tradeoffs Under Full Data

Abstract

We study a fine-grained model in which a perturbed version of some data ( $D$ ) is to be disclosed, with the aims of permitting the receiver to accurately infer some useful aspects ( $X=f(D)$ ) of it, while preventing her from inferring other private aspects ( $Y=g(D)$ ). Correlation between the bases for these inferences necessitates compromise between these goals. Determining exactly how the disclosure ( $M$ ) will be probabilistically generated (from $D$ ), somehow trading off between making $I(M;X)$ large and $I(M;Y)$ small, is cast as an algorithmic optimization problem. In 2013, Chakraborty et al. provided optimal solutions for the two extreme points on these objectives’ Pareto frontier: maximizing $I(M;X)$ s.t. $I(M;Y)=0$ (“perfect privacy,” via linear programming (LP)) and minimizing $I(M;Y)$ s.t. $H(X|M)=0$ (“perfect utility,” for which the trivial solution $M=X$ is optimal). We show that when minimizing $I(M;Y)-\beta I(M;X)$ , we can restrict ourselves w.l.o.g. to solutions satisfying several normal-form conditions, which leads to 1) an alternative convex programming formulation when $\beta \in [0,1]$ , which we provide a practical optimal algorithm for, and 2) proof that $M=X$ is actually optimal for all $\beta \geq 1$ . This solves the primary open problem posed by Chakraborty et al. (It also provides a faster solution than Chakraborty et al. 's LP for the “perfect privacy” special case.)