Privacy-Constrained Signals

TL;DR

This paper introduces a unified framework for characterizing signals under privacy constraints, decomposing feasible signals into minimal informative and privacy-preserving components, with applications to various privacy notions.

Contribution

It provides a complete characterization of minimal informative signals and a unified approach to different privacy constraints.

Findings

Decomposition of feasible signals into informative and privacy-preserving parts

Complete characterization of minimum informative signals

Application to differential and inferential privacy

Abstract

This paper provides a unified approach to characterize the set of all feasible signals subject to privacy constraints. The Blackwell frontier of feasible signals can be decomposed into minimum informative signals achieving the Blackwell frontier of privacy variables, and conditionally privacy-preserving signals. A complete characterization of the minimum informative signals is then provided. We apply the framework to ex-post privacy (including differential and inferential privacy) and to constraints on posterior means of arbitrary statistics.