Perfect Privacy and Strong Stationary Times for Markovian Sources

2026-01-23

AI Summary

This work addresses the problem of maximizing the amount of data released from a finite, time-homogeneous Markov source while preserving perfect information-theoretic privacy of the initial state. The authors propose a sequential data sharing strategy based on a deletion mechanism, where a strongly stationary time determines the deletion window to simultaneously achieve perfect privacy and optimal expected Hamming distortion. The key contribution lies in establishing that the optimal sequential deletion mechanism is equivalent to a fixed-window form and demonstrating that only a constant average number of data points— independent of the total sequence length \(N\)—needs to be deleted to satisfy both perfect privacy and optimal distortion performance.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We consider the problem of sharing correlated data under a perfect information-theoretic privacy constraint. We focus on redaction (erasure) mechanisms, in which data are either withheld or released unchanged, and measure utility by the average cardinality of the released set, equivalently, the expected Hamming distortion. Assuming the data are generated by a finite time-homogeneous Markov chain, we study the protection of the initial state while maximizing the amount of shared data. We establish a connection between perfect privacy and window-based redaction schemes, showing that erasing data up to a strong stationary time preserves privacy under suitable conditions. We further study an optimal sequential redaction mechanism and prove that it admits an equivalent window interpretation. Interestingly, we show that both mechanisms achieve the optimal distortion while redacting only a constant average number of data points, independent of the data length~$N$.

Problem

• Perfect Privacy
• Markovian Sources
• Redaction Mechanisms
• Strong Stationary Times
• Information-theoretic Privacy

Innovation

• Perfect Privacy
• Strong Stationary Time
• Redaction Mechanism
• Markovian Sources
• Information-Theoretic Privacy