🤖 AI Summary
This work addresses the challenge of robust mean estimation under outliers and heavy-tailed distributions while guaranteeing zero-concentrated differential privacy (zCDP). The authors propose a novel method termed “balloon mean,” which integrates iterative clipping with an expanded Mahalanobis-distance ball—referred to as a “balloon”—to achieve both robustness and computational feasibility. Designed for the contaminated ellipsoidal model, the approach requires only a small number of interpretable hyperparameters. Theoretical analysis establishes its statistical optimality and robustness in the presence of heavy-tailed noise and data contamination. Empirical evaluations demonstrate that the balloon mean significantly outperforms existing differentially private mean estimators across a variety of contamination scenarios.
📝 Abstract
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.