# Outlier-robust Estimation of a Sparse Linear Model Using Invexity

arXiv: https://arxiv.org/abs/2306.12678 · HTML: https://mlsanity.com/paper/2306.12678/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 22 Jun 2023.

## Builds on (most cited first, 8 of 8)

- [Adaptive Huber Regression](https://mlsanity.com/paper/1706.06991/) (2017)
- [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)
- [Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm](https://mlsanity.com/paper/1405.2936/) (2014)
- [Consistent Estimation for PCA and Sparse Regression with Oblivious Outliers](https://mlsanity.com/paper/2111.02966/) (2021)
- [Improved Imaging by Invex Regularizers with Global Optima Guarantees](https://mlsanity.com/paper/2211.10112/) (2022)
- [Fair Sparse Regression with Clustering: An Invex Relaxation for a Combinatorial Problem](https://mlsanity.com/paper/2102.09704/) (2021)
- [Sparse Mixed Linear Regression with Guarantees: Taming an Intractable Problem with Invex Relaxation](https://mlsanity.com/paper/2206.01167/) (2022)

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

- [Multi-Model 3D Registration: Finding Multiple Moving Objects in Cluttered Point Clouds](https://mlsanity.com/paper/2402.10865/) (2024)

## Abstract (arXiv)

In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of outlier-robust lasso which also identifies clean samples. Subsequently, we use these clean samples to make a good estimation. We also provide a novel invex relaxation for the combinatorial problem and provide provable theoretical guarantees for this relaxation. Finally, we conduct experiments to validate our theory and compare our results against standard lasso.