Computationally tractable robust differentially private mean estimation
For practitioners needing robust and private mean estimation under heavy-tailed or contaminated data, this method offers a practical improvement over existing differentially private estimators.
The paper introduces the balloon mean, a computationally tractable differentially private mean estimator that is robust to outliers, and demonstrates through theory and simulations that it outperforms existing methods in contaminated settings.
We develop a new, differentially private mean estimator called the balloon mean. The main features of the balloon mean are that it is computationally tractable and enjoys robustness to outlying observations. It is based on an iterative clipping procedure over expanding Mahalanobis balls, or ``balloons.'' The method satisfies zero-concentrated differential privacy and depends on a small number of interpretable tuning parameters. We provide theoretical guarantees under heavy-tailed and contaminated elliptical models, characterizing its statistical performance and robustness to outliers. Extensive simulations demonstrate that the balloon mean is robust to heavy-tailed and contaminated data, and outperforms existing differentially private mean estimators in contaminated settings.