Differential Privacy for Symbolic Systems with Application to Markov Chains

TL;DR

This paper introduces a novel differential privacy framework tailored for symbolic data and Markov chains, enabling privacy-preserving trajectory generation with proven accuracy bounds and efficient mechanisms.

Contribution

It develops new differential privacy mechanisms for symbolic sequences and Markov chains, extending privacy protections to non-numerical data types.

Findings

Efficient offline and online privacy mechanisms for symbolic data.

Accuracy bounds for privacy-preserving string and sequence generation.

Numerical validation demonstrating effectiveness on English words.

Abstract

Data-driven systems are gathering increasing amounts of data from users, and sensitive user data requires privacy protections. In some cases, the data gathered is non-numerical or symbolic, and conventional approaches to privacy, e.g., adding noise, do not apply, though such systems still require privacy protections. Accordingly, we present a novel differential privacy framework for protecting trajectories generated by symbolic systems. These trajectories can be represented as words or strings over a finite alphabet. We develop new differential privacy mechanisms that approximate a sensitive word using a random word that is likely to be near it. An offline mechanism is implemented efficiently using a Modified Hamming Distance Automaton to generate whole privatized output words over a finite time horizon. Then, an online mechanism is implemented by taking in a sensitive symbol and generating a randomized output symbol at each timestep. This work is extended to Markov chains to generate differentially private state sequences that a given Markov chain could have produced. Statistical accuracy bounds are developed to quantify the accuracy of these mechanisms, and numerical results validate the accuracy of these techniques for strings of English words.