Privacy-Utility Tradeoffs under Constrained Data Release Mechanisms

TL;DR

This paper investigates how constraints on available data affect the optimal privacy-utility tradeoff in data release mechanisms, revealing hierarchy relations and conditions for equivalence under various data availability scenarios.

Contribution

It introduces a hierarchy of privacy-utility tradeoff regions based on data availability and characterizes conditions for their equivalence, extending understanding of privacy-utility tradeoffs under data constraints.

Findings

Hierarchy of tradeoff regions based on data availability

Conditions for tradeoff region equivalence using common information

Closed-form expressions for specific privacy and utility measures

Abstract

Privacy-preserving data release mechanisms aim to simultaneously minimize information-leakage with respect to sensitive data and distortion with respect to useful data. Dependencies between sensitive and useful data results in a privacy-utility tradeoff that has strong connections to generalized rate-distortion problems. In this work, we study how the optimal privacy-utility tradeoff region is affected by constraints on the data that is directly available as input to the release mechanism. In particular, we consider the availability of only sensitive data, only useful data, and both (full data). We show that a general hierarchy holds: the tradeoff region given only the sensitive data is no larger than the region given only the useful data, which in turn is clearly no larger than the region given both sensitive and useful data. In addition, we determine conditions under which the tradeoff region given only the useful data coincides with that given full data. These are based on the common information between the sensitive and useful data. We establish these results for general families of privacy and utility measures that satisfy certain natural properties required of any reasonable measure of privacy or utility. We also uncover a new, subtler aspect of the data processing inequality for general non-symmetric privacy measures and discuss its operational relevance and implications. Finally, we derive exact closed-analytic-form expressions for the privacy-utility tradeoffs for symmetrically dependent sensitive and useful data under mutual information and Hamming distortion as the respective privacy and utility measures.