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.

翻译：我们提出了一种新的差分隐私均值估计器，称为"气球均值"。该方法的主要特点在于其计算可行且对异常观测值具有鲁棒性。该估计器基于对不断扩大的马氏距离球（即"气球"）进行迭代裁剪的过程。该方法满足零集中差分隐私，并依赖于少量可解释的调优参数。我们在重尾和污染椭圆模型下提供了理论保证，刻画了其统计性能和对异常值的鲁棒性。大量模拟实验表明，气球均值对重尾和污染数据具有鲁棒性，且在污染场景下优于现有的差分隐私均值估计器。