# Robust Distributed High-Dimensional Regression: A Convoluted Rank Approach

## TL;DR

This paper introduces a robust regression method for high-dimensional data in distributed systems, effective even with noisy or outlier-prone data.

## Contribution

A novel convoluted rank regression method with non-asymptotic error bounds for distributed settings and sparse regimes.

## Key findings

- The proposed estimator achieves minimax-optimal convergence after logarithmic communication rounds.
- Simulations show stable performance across various error distributions with accurate coefficient estimation.
- The method supports fast optimization in high-dimensional and distributed environments.

## Abstract

This paper investigates robust high-dimensional convoluted rank regression in distributed environments. We propose an estimation method suitable for sparse regimes, which remains effective under heavy-tailed errors and outliers, as it does not impose moment assumptions on the noise distribution. To facilitate scalable computation, we develop a local linear approximation algorithm, enabling fast and stable optimization in high-dimensional settings and across distributed systems. Our theoretical results provide non-asymptotic error bounds for both one-round and multi-round communication schemes, explicitly quantifying how estimation accuracy improves with additional communication rounds. Specifically, after a number of communication rounds (logarithmic in the number of machines), the proposed estimator achieves the minimax-optimal convergence rate, up to logarithmic factors. Extensive simulations further demonstrate stable performance across a wide range of error distributions, with accurate coefficient estimation and reliable support recovery.