Differentially Private Data-Driven Markov Chain Modeling

TL;DR

This paper presents a differentially private method for generating accurate Markov chain models from user data, ensuring privacy while maintaining high fidelity in the modeled behavior.

Contribution

It introduces a novel differential privacy technique for stochastic matrices and provides theoretical bounds and simulations demonstrating minimal impact on model accuracy.

Findings

Less than 2% error in stationary distribution under typical privacy settings

The method effectively privatizes Markov chain models without significant loss of fidelity

Theoretical bounds on accuracy and convergence rate changes are established

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.