Bounding the Excess Risk for Linear Models Trained on Marginal-Preserving, Differentially-Private, Synthetic Data
This addresses privacy concerns for individuals contributing to training datasets, though it is incremental as it focuses on linear models with specific loss functions.
The paper tackles the problem of preventing private information leakage in machine learning by training linear models on differentially-private synthetic data that preserves low-order marginals, and provides novel theoretical bounds on the excess empirical risk with experimental validation.
The growing use of machine learning (ML) has raised concerns that an ML model may reveal private information about an individual who has contributed to the training dataset. To prevent leakage of sensitive data, we consider using differentially-private (DP), synthetic training data instead of real training data to train an ML model. A key desirable property of synthetic data is its ability to preserve the low-order marginals of the original distribution. Our main contribution comprises novel upper and lower bounds on the excess empirical risk of linear models trained on such synthetic data, for continuous and Lipschitz loss functions. We perform extensive experimentation alongside our theoretical results.