# Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliers

arXiv: https://arxiv.org/abs/2408.01336 · HTML: https://mlsanity.com/paper/2408.01336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 2 Aug 2024.

## Builds on (most cited first, 21 of 21)

- [Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixtures](https://mlsanity.com/paper/1611.03473/) (2016)
- [Adaptive Huber Regression](https://mlsanity.com/paper/1706.06991/) (2017)
- [Statistical Query Algorithms and Low-Degree Tests Are Almost Equivalent](https://mlsanity.com/paper/2009.06107/) (2020)
- [Robust regression with covariate filtering: Heavy tails and adversarial contamination](https://mlsanity.com/paper/2009.12976/) (2020)
- [Robust Linear Regression: Optimal Rates in Polynomial Time](https://mlsanity.com/paper/2007.01394/) (2020)
- [Subexponential-Time Algorithms for Sparse PCA](https://mlsanity.com/paper/1907.11635/) (2019)
- [Computational Barriers to Estimation from Low-Degree Polynomials](https://mlsanity.com/paper/2008.02269/) (2020)
- [Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimator](https://mlsanity.com/paper/1904.06288/) (2019)
- [High Dimensional Robust Sparse Regression](https://mlsanity.com/paper/1805.11643/) (2018)
- [Statistical and computational trade-offs in estimation of sparse principal components](https://mlsanity.com/paper/1408.5369/) (2014)
- [Robust Sparse Mean Estimation via Sum of Squares](https://mlsanity.com/paper/2206.03441/) (2022)
- [A Shrinkage Principle for Heavy-Tailed Data: High-Dimensional Robust Low-Rank Matrix Recovery](https://mlsanity.com/paper/1603.08315/) (2016)
- [User-Friendly Covariance Estimation for Heavy-Tailed Distributions](https://mlsanity.com/paper/1811.01520/) (2018)
- [Outlier-Robust Sparse Mean Estimation for Heavy-Tailed Distributions](https://mlsanity.com/paper/2211.16333/) (2022)
- [Computationally efficient sparse clustering](https://mlsanity.com/paper/2005.10817/) (2020)
- [Robust Inference via Multiplier Bootstrap](https://mlsanity.com/paper/1903.07208/) (2019)
- [Statistical-Computational Tradeoffs in Mixed Sparse Linear Regression](https://mlsanity.com/paper/2303.02118/) (2023)
- [Curse of Heterogeneity: Computational Barriers in Sparse Mixture Models and Phase Retrieval](https://mlsanity.com/paper/1808.06996/) (2018)
- [Generic Error Bounds for the Generalized Lasso with Sub-Exponential Data](https://mlsanity.com/paper/2004.05361/) (2020)
- [Robust Methods for High-Dimensional Linear Learning](https://mlsanity.com/paper/2208.05447/) (2022)
- [Outlier Robust and Sparse Estimation of Linear Regression Coefficients](https://mlsanity.com/paper/2208.11592/) (2022)

## Abstract (arXiv)

We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and noises are sampled from heavy tailed distributions but also contaminated by outliers. Our estimators can be computed efficiently, and exhibit sharp error bounds.