Natural Privacy Filters Are Not Always Free: A Characterization of Free Natural Filters

2026-02-17

AI Summary

This study investigates whether natural privacy filters can always be implemented without loss in adaptively composed differentially private mechanisms. By integrating frameworks from differential privacy, Rényi differential privacy, and Gaussian differential privacy, and by introducing the notions of privacy profiles and order-theoretic characterizations of mechanism composition, the work establishes—for the first time—that natural privacy filters are not universally "free." Lossless filtering is achievable only when the family of mechanisms exhibits a well-behaved order structure under composition. This result delineates the precise applicability boundary of natural privacy filters and provides a theoretical foundation for constructing adaptive compositions of privacy-preserving mechanisms that are both efficient and rigorously secure.

Technology Category

• Machine Learning: Privacy
• Natural Language Processing: Ethics — Bias, Fairness, Transparency & Privacy
• Computer Vision: Bias, Fairness & Privacy

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We study natural privacy filters, which enable the exact composition of differentially private (DP) mechanisms with adaptively chosen privacy characteristics. Earlier privacy filters consider only simple privacy parameters such as Rényi-DP or Gaussian DP parameters. Natural filters account for the entire privacy profile of every query, promising greater utility for a given privacy budget. We show that, contrary to other forms of DP, natural privacy filters are not free in general. Indeed, we show that only families of privacy mechanisms that are well-ordered when composed admit free natural privacy filters.

Problem

• natural privacy filters
• differential privacy
• privacy composition
• adaptive mechanisms
• privacy profiles

Innovation

• natural privacy filters
• differential privacy
• privacy profile
• adaptive composition
• well-ordered mechanisms