Optimal Local Bayesian Differential Privacy over Markov Chains

TL;DR

This paper introduces an optimal local Bayesian differential privacy mechanism for binary Markov chain data, improving privacy-utility tradeoffs and demonstrating robustness through experiments on synthetic and real data.

Contribution

It provides a new mechanism achieving optimal noise-privacy tradeoffs for Bayesian differential privacy in Markov chain data, surpassing previous methods.

Findings

The mechanism achieves the best possible privacy-utility tradeoff.

It outperforms existing BDP mechanisms in Markov chain settings.

Experiments show robustness of privacy guarantees on real-world data.

Abstract

In the literature of data privacy, differential privacy is the most popular model. An algorithm is differentially private if its outputs with and without any individual's data are indistinguishable. In this paper, we focus on data generated from a Markov chain and argue that Bayesian differential privacy (BDP) offers more meaningful guarantees in this context. Our main theoretical contribution is providing a mechanism for achieving BDP when data is drawn from a binary Markov chain. We improve on the state-of-the-art BDP mechanism and show that our mechanism provides the optimal noise-privacy tradeoffs for any local mechanism up to negligible factors. We also briefly discuss a non-local mechanism which adds correlated noise. Lastly, we perform experiments on synthetic data that detail when DP is insufficient, and experiments on real data to show that our privacy guarantees are robust to underlying distributions that are not simple Markov chains.