Differentially Private Methods for Compositional Data

TL;DR

This paper develops and compares differentially private methods for analyzing compositional data, focusing on Bayesian and bootstrap approaches using the Dirichlet distribution, with applications to real survey data.

Contribution

It introduces novel differentially private techniques tailored for compositional data analysis, including Bayesian and bootstrap methods, and evaluates their performance through simulations and real data application.

Findings

Bayesian methods outperform bootstrap in privacy-utility trade-offs.

Approximate Bayesian Computation offers a computationally efficient alternative.

Methodologies successfully applied to American Time Use Survey data.

Abstract

Confidential data, such as electronic health records, activity data from wearable devices, and geolocation data, are becoming increasingly prevalent. Differential privacy provides a framework to conduct statistical analyses while mitigating the risk of leaking private information. Compositional data, which consist of vectors with positive components that add up to a constant, have received little attention in the differential privacy literature. This article proposes differentially private approaches for analyzing compositional data using the Dirichlet distribution. We explore several methods, including Bayesian and bootstrap procedures. For the Bayesian methods, we consider posterior inference techniques based on Markov Chain Monte Carlo, Approximate Bayesian Computation, and asymptotic approximations. We conduct an extensive simulation study to compare these approaches and make evidence-based recommendations. Finally, we apply the methodology to a data set from the American Time Use Survey.