Differential Privacy and Survey Sampling

TL;DR

This paper links the Horvitz-Thompson estimator to differential privacy, providing formulas to determine privacy parameters and noise scale for sampling mechanisms, especially in binary data scenarios.

Contribution

It introduces formulas to compute differential privacy parameters for the Horvitz-Thompson estimator, enabling privacy-preserving sampling with controlled noise addition.

Findings

Formulas for epsilon and delta parameters derived for the estimator

Guidelines for adding Laplace or Gaussian noise to achieve desired privacy levels

Special case formulas for simple random sampling on binary data

Abstract

The Horvitz-Thompson estimate of a total can be seen as as differentially private mechanism applied to this population total. We provide forumlae to compute the $\epsilon$ and $\delta$ parameter for this specific mecanism, coupled or not coupled with the addition of a Laplace or a Gaussian noise. This allows to determine the scale of the Laplace privacy mechanism to be added to reach a specified level of privacy, expressed in terms of $\epsilon,\delta$ differential privacy. In particular, we provide simple formulae for the special case of simple random sampling on binary data.