# Iteratively Reweighted ℓ1-Penalized Robust Regression

arXiv: https://arxiv.org/abs/1907.04027 · HTML: https://mlsanity.com/paper/1907.04027/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Robust Variable Selection and Estimation Via Adaptive Elastic Net S-Estimators for Linear Regression](https://mlsanity.com/paper/2107.03325/) (2021)

## Abstract (arXiv)

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moment, we show that iteratively reweighted ℓ1-penalized adaptive Huber regression estimator satisfies exponential deviation bounds and oracle properties, including the oracle convergence rate and variable selection consistency, under a weak beta-min condition. Computationally, we need as many as O(log s + loglog d) iterations to reach such an oracle estimator, where s and d denote the sparsity and ambient dimension, respectively. Extension to a general class of robust loss functions is also considered. Numerical studies lend strong support to our methodology and theory.