New Differentially Private Mean Estimator Balances Computational Efficiency and Robustness to Outliers
Researchers have introduced a new differentially private mean estimator called the 'balloon mean,' designed to be both computationally efficient and robust to outliers. The method uses an iterative clipping procedure over expanding Mahalanobis balls and satisfies zero-concentrated differential privacy. It addresses a key gap in privacy-preserving statistics, where existing estimators tend to perform poorly in the presence of contaminated or heavy-tailed data.
A new statistical method called the balloon mean has been proposed for differentially private mean estimation, combining computational tractability with robustness to outlying observations. The estimator works by iteratively clipping data points within expanding Mahalanobis balls—geometric regions that account for the shape of the data distribution—rather than applying a fixed clipping threshold. It satisfies zero-concentrated differential privacy, a strong formal privacy guarantee, and requires only a small number of interpretable tuning parameters. The authors provide theoretical guarantees under heavy-tailed and contaminated elliptical models, characterizing both statistical performance and robustness properties. Extensive simulations across 40 pages and 17 figures reportedly show the balloon mean outperforms existing differentially private mean estimators specifically in contaminated data settings, though performance under clean, well-behaved distributions is not highlighted as a primary advantage.
What's missing
As a preprint, this work has not yet undergone peer review, so the theoretical claims and simulation results have not been independently validated. The paper does not appear to include real-world empirical benchmarks beyond simulations, leaving open questions about practical performance on actual sensitive datasets.
What different sources said
- arXiv stat.MLCenter
Computationally tractable robust differentially private mean estimation
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