Privacy Amplification Through Synthetic Data: Insights from Linear Regression
This provides theoretical insights into privacy risks and benefits in synthetic data generation, though it is incremental as it focuses on linear regression as a foundational case.
The paper investigates privacy amplification in synthetic data generation through linear regression, showing that when the generative model's seed is controlled by an adversary, a single synthetic data point can leak as much information as releasing the model, but when generated from random inputs, releasing limited synthetic data points amplifies privacy beyond the model's inherent guarantees.
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.