Privacy-Constrained Signals

2025-11-26

AI Summary

This paper investigates the structural characterization of feasible signal sets under privacy constraints. Methodologically, it introduces a unified framework that decomposes any feasible signal into two orthogonal components: a minimal-information signal and a conditional privacy-preserving signal—thereby fully characterizing the Blackwell frontier of the privacy variable. The framework integrates Blackwell’s theory of statistical information comparison, a general posterior-based privacy model (encompassing both differential privacy and inference privacy), and posterior-mean constraints on statistics. Crucially, it is agnostic to the specific privacy definition, ensuring broad applicability. The contribution is threefold: (i) it reveals the fundamental structure underlying the privacy–information trade-off; (ii) it derives a tight information-theoretic lower bound on signal informativeness under privacy constraints; and (iii) it establishes a rigorous theoretical foundation for designing and analyzing privacy mechanisms.

Technology Category

Machine Learning: PrivacyGame Theory and Economic Paradigms: Mechanism DesignReasoning under Uncertainty: Stochastic Optimization

Application Category

Security and Privacy: Privacy-enhancing technologiesUser Modeling, Personalization and Recommendation: User privacy protection in personalized systemsEconomics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

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.

Problem

• Characterizing feasible signals under privacy constraints using unified approach
• Decomposing Blackwell frontier into minimum informative and privacy-preserving signals
• Applying framework to differential privacy and posterior mean constraints

Innovation

• Unified approach for privacy-constrained feasible signals
• Decomposing Blackwell frontier into minimum informative signals
• Complete characterization of minimum informative privacy signals