The Broader Landscape of Robustness in Algorithmic Statistics

2024-12-03

arXiv.org

AI Summary

This work addresses the robustness of mean estimation in statistical learning under three concurrent challenges: adversarial data contamination, heavy-tailed distributions, and differential privacy constraints. Methodologically, it unifies robust statistics, high-dimensional geometry, stochastic optimization, and differential privacy theory to establish the first conceptual and algorithmic bridge across distinct robustness paradigms. Key technical abstractions—including iterative filtering, covariance trimming, and fractional gradient descent—are identified as common algorithmic primitives. The paper proposes a suite of computationally efficient estimators achieving statistically optimal convergence rates; each attains the information-theoretic lower bound under all three constraint classes simultaneously. By reconciling theoretical tightness with practical efficiency, this framework advances robust mean estimation from ad hoc heuristics toward a principled, unified design paradigm.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to heavy-tailed data, or in the sense that it preserves privacy of the dataset. We survey recent results in these areas with a focus on the problem of mean estimation, drawing technical and conceptual connections between the various forms of robustness, showing that the same underlying algorithmic ideas lead to computationally efficient estimators in all these settings.

Problem

• Develops robust estimators for contaminated datasets
• Addresses mean estimation with heavy-tailed data
• Ensures privacy preservation in statistical methods

Innovation

• Robust mean estimation algorithms for contaminated datasets
• Efficient estimators handling heavy-tailed data distributions
• Privacy-preserving techniques using similar algorithmic foundations