Differentially Private Synthetic Heavy-tailed Data

TL;DR

This paper introduces a differential privacy framework using the K-Norm Gradient Mechanism with quantile regression to generate synthetic heavy-tailed data, ensuring privacy and high utility for economic research datasets.

Contribution

It proposes a novel DP synthetic data generation method tailored for heavy-tailed data using KNG and quantile regression, with an efficient stepwise implementation.

Findings

Achieves better utility than existing KNG methods at the same privacy level.

Successfully applied to the Synthetic Longitudinal Business Database.

Demonstrates strong privacy guarantees with high data utility.

Abstract

The U.S. Census Longitudinal Business Database (LBD) product contains employment and payroll information of all U.S. establishments and firms dating back to 1976 and is an invaluable resource for economic research. However, the sensitive information in LBD requires confidentiality measures that the U.S. Census in part addressed by releasing a synthetic version (SynLBD) of the data to protect firms' privacy while ensuring its usability for research activities, but without provable privacy guarantees. In this paper, we propose using the framework of differential privacy (DP) that offers strong provable privacy protection against arbitrary adversaries to generate synthetic heavy-tailed data with a formal privacy guarantee while preserving high levels of utility. We propose using the K-Norm Gradient Mechanism (KNG) with quantile regression for DP synthetic data generation. The proposed methodology offers the flexibility of the well-known exponential mechanism while adding less noise. We propose implementing KNG in a stepwise and sandwich order, such that new quantile estimation relies on previously sampled quantiles, to more efficiently use the privacy-loss budget. Generating synthetic heavy-tailed data with a formal privacy guarantee while preserving high levels of utility is a challenging problem for data curators and researchers. However, we show that the proposed methods can achieve better data utility relative to the original KNG at the same privacy-loss budget through a simulation study and an application to the Synthetic Longitudinal Business Database.