Robust Mean Estimation under Quantization

2026-01-11

AI Summary

This study addresses the problem of multivariate mean estimation under simultaneous quantization constraints and adversarial contamination. Focusing on two canonical settings—single-bit quantization and partial unquantized observations—the work proposes a robust mean estimator that integrates multivariate robust statistics, quantization-aware processing, and adversarial robustness design. Theoretical analysis demonstrates that the proposed estimator achieves nearly minimax-optimal error rates in both quantization regimes, with suboptimality limited only by logarithmic factors. This result substantially advances the theoretical and practical boundaries of high-dimensional robust estimation under severely restricted observational conditions.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Intelligent Robots: State Estimation
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We consider the problem of mean estimation under quantization and adversarial corruption. We construct multivariate robust estimators that are optimal up to logarithmic factors in two different settings. The first is a one-bit setting, where each bit depends only on a single sample, and the second is a partial quantization setting, in which the estimator may use a small fraction of unquantized data.

Problem

• robust mean estimation
• quantization
• adversarial corruption
• multivariate estimation

Innovation

• robust mean estimation
• quantization
• adversarial corruption
• one-bit sensing
• partial quantization