Computationally tractable robust differentially private mean estimation

2026-06-12 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Cybersecurity & Data Privacy, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

A new differentially private mean estimator, termed the "balloon mean," has been developed to address limitations in existing robust and private mean estimation methods. This estimator is computationally tractable, operating in O(d^3 + nd^2 + Mnd + Mn log n) time, and offers robustness against outlying observations. It employs an iterative clipping procedure over expanding Mahalanobis balls, satisfying rho-zero-concentrated differential privacy. Theoretical guarantees are provided for heavy-tailed and contaminated elliptical models, characterizing its statistical performance. Extensive simulations, across dimensions d (e.g., 8, 64, 128), sample sizes n (e.g., 250-5000), and privacy budgets rho (0.01, 0.1, 1), demonstrate its robustness to heavy-tailed and eta=0.1 contaminated data. The balloon mean consistently outperforms existing differentially private mean estimators in contaminated settings, showing low sensitivity to tuning parameters like initial mean, radius, grid size (beta=1.01), and number of iterations (M=4).

Key takeaway

For Machine Learning Engineers or AI Scientists working with sensitive, high-dimensional datasets, the balloon mean offers a robust and computationally efficient solution for private mean estimation. You should consider implementing this iterative Mahalanobis clipping method, especially when dealing with heavy-tailed or adversarially contaminated data. Its low sensitivity to tuning parameters simplifies deployment, and adjusting the tau parameter can optimize robustness for your specific contamination levels.

Key insights

The balloon mean offers a computationally efficient and robust method for differentially private mean estimation using iterative Mahalanobis clipping.

Principles

• Iterative clipping improves robustness and mitigates poor initial values.
• Smaller tau values enhance robustness against adversarial contamination.
• Logarithmic dependence on parameters implies low tuning sensitivity.

Method

Iteratively project data onto expanding Mahalanobis balls, compute noisy mean of projections, then privately adjust balloon radius to contain a tau fraction of data.

In practice

• Use M=4 iterations for high-dimensional data.
• Employ decreasing tau schedules for improved robustness in contaminated settings.
• Consider tau < 0.9 for high-dimensional scenarios.

Topics

• Differential Privacy
• Robust Statistics
• Mean Estimation
• Mahalanobis Distance
• Data Contamination
• Zero-Concentrated DP

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Security Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.