Differentially Private Data-Driven Markov Chain Modeling

2026-02-25

AI Summary

This work addresses the challenge of accurately modeling data-driven Markov chains while preserving user privacy. The authors propose a novel differential privacy mechanism that, for the first time, applies privacy-preserving perturbations to database queries within the simplex space and extends this approach to stochastic transition matrices whose rows are probability simplices. Through rigorous theoretical analysis, they characterize the impact of privacy-inducing noise on the stationary distribution and convergence rate of the resulting Markov chain, deriving error bounds in terms of Kullback–Leibler divergence. Experimental results demonstrate that under standard privacy parameters, the stationary distribution incurs less than 2% error, effectively preserving the behavioral characteristics of the original system even under strong privacy guarantees.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Stochastic Optimization
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Markov chains model a wide range of user behaviors. However, generating accurate Markov chain models requires substantial user data, and sharing these models without privacy protections may reveal sensitive information about the underlying user data. We introduce a method for protecting user data used to formulate a Markov chain model. First, we develop a method for privatizing database queries whose outputs are elements of the unit simplex, and we prove that this method is differentially private. We quantify its accuracy by bounding the expected KL divergence between private and non-private queries. We extend this method to privatize stochastic matrices whose rows are each a simplex-valued query of a database, which includes data-driven Markov chain models. To assess their accuracy, we analytically bound the change in the stationary distribution and the change in the convergence rate between a non-private Markov chain model and its private form. Simulations show that under a typical privacy implementation, our method yields less than 2% error in the stationary distribution, indicating that our approach to private modeling faithfully captures the behavior of the systems we study.

Problem

• Differential Privacy
• Markov Chain
• User Data Privacy
• Stochastic Matrix
• Data-Driven Modeling

Innovation

• Differential Privacy
• Markov Chain
• Simplex-Valued Query
• Stationary Distribution
• Stochastic Matrix