# Distributed Adaptive Huber Regression

arXiv: https://arxiv.org/abs/2107.02726 · HTML: https://mlsanity.com/paper/2107.02726/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2021.

## Built on by (most cited first, 2 of 2)

- [Distributed Estimation and Inference for Semi-parametric Binary Response Models](https://mlsanity.com/paper/2210.08393/) (2022)
- [Byzantine-Robust Distributed Sparse Learning Revisited](https://mlsanity.com/paper/2605.13283/) (2026)

## Abstract (arXiv)

Distributed data naturally arise in scenarios involving multiple sources of observations, each stored at a different location. Directly pooling all the data together is often prohibited due to limited bandwidth and storage, or due to privacy protocols. This paper introduces a new robust distributed algorithm for fitting linear regressions when data are subject to heavy-tailed and/or asymmetric errors with finite second moments. The algorithm only communicates gradient information at each iteration and therefore is communication-efficient. Statistically, the resulting estimator achieves the centralized nonasymptotic error bound as if all the data were pooled together and came from a distribution with sub-Gaussian tails. Under a finite (2+δ)-th moment condition, we derive a Berry-Esseen bound for the distributed estimator, based on which we construct robust confidence intervals. Numerical studies further confirm that compared with extant distributed methods, the proposed methods achieve near-optimal accuracy with low variability and better coverage with tighter confidence width.