Privacy Against Statistical Inference

TL;DR

This paper introduces a comprehensive information-theoretic framework for quantifying privacy in data sharing, proposing new metrics and optimization methods that relate privacy to utility constraints and comparing with differential privacy.

Contribution

It develops a general statistical inference framework for privacy, introduces two new privacy metrics, and formulates the optimal privacy-preserving data mapping as a convex rate-distortion problem.

Findings

The framework captures privacy threats using information-theoretic measures.

Optimal privacy-preserving mappings can be found via convex optimization.

The approach offers a non-asymptotic analysis contrasting differential privacy.

Abstract

We propose a general statistical inference framework to capture the privacy threat incurred by a user that releases data to a passive but curious adversary, given utility constraints. We show that applying this general framework to the setting where the adversary uses the self-information cost function naturally leads to a non-asymptotic information-theoretic approach for characterizing the best achievable privacy subject to utility constraints. Based on these results we introduce two privacy metrics, namely average information leakage and maximum information leakage. We prove that under both metrics the resulting design problem of finding the optimal mapping from the user's data to a privacy-preserving output can be cast as a modified rate-distortion problem which, in turn, can be formulated as a convex program. Finally, we compare our framework with differential privacy.