Privacy Amplification Through Synthetic Data: Insights from Linear Regression

TL;DR

This paper investigates how synthetic data can enhance privacy in linear regression, revealing conditions under which privacy amplification occurs or fails, and providing theoretical insights into privacy guarantees.

Contribution

It offers the first rigorous theoretical analysis of privacy amplification through synthetic data in linear regression, identifying scenarios of both privacy leakage and amplification.

Findings

Single synthetic data point can leak as much information as the model if seed is controlled.

Releasing limited synthetic data from random inputs can amplify privacy beyond model guarantees.

The results establish a foundation for future general privacy bounds in synthetic data use.

Abstract

Synthetic data inherits the differential privacy guarantees of the model used to generate it. Additionally, synthetic data may benefit from privacy amplification when the generative model is kept hidden. While empirical studies suggest this phenomenon, a rigorous theoretical understanding is still lacking. In this paper, we investigate this question through the well-understood framework of linear regression. First, we establish negative results showing that if an adversary controls the seed of the generative model, a single synthetic data point can leak as much information as releasing the model itself. Conversely, we show that when synthetic data is generated from random inputs, releasing a limited number of synthetic data points amplifies privacy beyond the model's inherent guarantees. We believe our findings in linear regression can serve as a foundation for deriving more general bounds in the future.