Balloon Mean: New differentially private estimator handles outliers efficiently
A computationally tractable DP mean estimator that beats existing methods on contaminated data.
Differentially private (DP) mean estimation is critical for privacy-preserving data analysis, but traditional methods struggle with outliers and heavy-tailed distributions. In a new arXiv paper, Kelly Ramsay introduces the 'balloon mean,' an estimator that tackles both challenges head-on. The method works by iteratively clipping observations within expanding Mahalanobis balls (hence 'balloons'), gradually excluding outliers while satisfying zero-concentrated DP (zCDP). It requires only a few interpretable tuning parameters and runs efficiently, making it practical for real-world deployments.
Theoretical results show the balloon mean achieves strong statistical performance under heavy-tailed elliptical models and is robust to contamination. Extensive simulations confirm it outperforms existing DP mean estimators—such as the trimmed mean and Winsorized mean—in high-outlier regimes, while maintaining privacy guarantees. This work is especially relevant for industries like healthcare and finance, where data naturally contains anomalies and privacy is paramount. By combining robustness with formal differential privacy, the balloon mean enables more reliable insights from sensitive datasets.
- Iterative clipping over expanding Mahalanobis balls ('balloons') to handle outliers
- Satisfies zero-concentrated differential privacy (zCDP) with few interpretable tuning parameters
- Outperforms existing DP mean estimators in heavy-tailed and contaminated settings in simulations
Why It Matters
Enables robust, private mean estimation for real-world data with outliers, improving analytics without compromising privacy.