# Robust Mean Estimation under Quantization

arXiv: https://arxiv.org/abs/2601.07074 · HTML: https://mlsanity.com/paper/2601.07074/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 11 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Robust subgaussian estimation of a mean vector in nearly linear time](https://mlsanity.com/paper/1906.03058/) (2019)
- [Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms](https://mlsanity.com/paper/2001.08877/) (2020)
- [Correlated quantization for distributed mean estimation and optimization](https://mlsanity.com/paper/2203.04925/) (2022)
- [Covariance Estimation: Optimal Dimension-free Guarantees for Adversarial Corruption and Heavy Tails](https://mlsanity.com/paper/2205.08494/) (2022)
- [High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization](https://mlsanity.com/paper/2202.13157/) (2022)
- [The Generalized Lasso for Sub-gaussian Measurements with Dithered Quantization](https://mlsanity.com/paper/1807.06976/) (2018)
- [Mean Estimation from One-Bit Measurements](https://mlsanity.com/paper/1901.03403/) (2019)
- [Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2509.21940/) (2025)
- [On Quantizer Design for Distributed Bayesian Estimation in Sensor Networks](https://mlsanity.com/paper/1407.7152/) (2014)
- [A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate](https://mlsanity.com/paper/2308.16059/) (2023)
- [Distributed Sparse Normal Means Estimation with Sublinear Communication](https://mlsanity.com/paper/2102.03060/) (2021)

## Built on by (most cited first, 5 of 5)

- [Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes](https://mlsanity.com/paper/2604.07796/) (2026)
- [Open Problem: Is Interaction Necessary for Order-Optimal 1-bit Mean Estimation?](https://mlsanity.com/paper/2607.02896/) (2026)
- [Interaction Is Not Necessary for Order-Optimal 1-Bit Mean Estimation](https://mlsanity.com/paper/2608.02538/) (2026)
- [One-Bit Clustering for Two Component Sub-Gaussian Mixture Models](https://mlsanity.com/paper/2606.21873/) (2026)
- [Non-Adaptive 1-Bit Mean Estimation: Minimax Rates and the Sample-Interval Tradeoff](https://mlsanity.com/paper/2609.08564/) (2026)

## Abstract (arXiv)

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.