# Sparse linear regression from perturbed data

arXiv: https://arxiv.org/abs/2003.14389 · HTML: https://mlsanity.com/paper/2003.14389/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [One-Bit Compressive Sensing: Can We Go Deep and Blind?](https://mlsanity.com/paper/2203.11278/) (2022)
- [Compressive Recovery of Signals Defined on Perturbed Graphs](https://mlsanity.com/paper/2402.07637/) (2024)
- [Robust Non-adaptive Group Testing under Errors in Group Membership Specifications](https://mlsanity.com/paper/2409.05345/) (2024)
- [A fast algorithm for solving the lasso problem exactly without homotopy using differential inclusions](https://mlsanity.com/paper/2507.05562/) (2025)

## Abstract (arXiv)

The problem of sparse linear regression is relevant in the context of linear system identification from large datasets. When data are collected from real-world experiments, measurements are always affected by perturbations or low-precision representations. However, the problem of sparse linear regression from fully-perturbed data is scarcely studied in the literature, due to its mathematical complexity. In this paper, we show that, by assuming bounded perturbations, this problem can be tackled by solving low-complex l2 and l1 minimization problems. Both theoretical guarantees and numerical results are illustrated in the paper.