Differentially Private Methods for Compositional Data

Protecting individuals' private information while still allowing modelers to draw inferences from confidential data sets is a concern of many data producers. Differential privacy is a framework that enables statistical analyses while controlling the potential leakage of private information. Prior work has focused on proposing differentially private statistical methods for various types of confidential data. However, almost no existing work has focused on the analysis of compositional data. In this article, we investigate differentially private approaches for analyzing compositional data using the Dirichlet distribution as the statistical model. We consider several methods, including frequentist and Bayesian procedures, along with computational strategies. We assess the approaches' performance using simulated data and illustrate their usefulness by applying them to data from the American Time Use Survey.