We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes. We demonstrate the effectiveness of our algorithms both theoretically and empirically using synthetic and real-world datasets -- showing that their asymptotic error rates match the state-of-the-art theoretical bounds, and that they concretely outperform all previous methods. Specifically, previous estimators either have weak empirical accuracy at small sample sizes, perform poorly for multivariate data, or require the user to provide strong a priori estimates for the parameters.

翻译：我们提出了针对多元亚高斯数据均值与协方差的简洁差分隐私估计器，该估计器在小样本量下仍能保持较高精度。我们通过合成数据集与真实世界数据集，从理论与实证两方面验证了算法的有效性——结果表明其渐近误差率达到了最先进的理论界限，且在实际表现上全面超越了以往所有方法。具体而言，先前估计器或在小样本量下实证精度较弱，或在多元数据上表现欠佳，或需要用户提供较强的参数先验估计。