2013/10/28 by Salvador Flores, Flores, Salvador, Luis M. Briceño-Arias +2
Engineering · Mathematics · #62F35 #65K05 #90C31 #94B35 #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #math.OC #msc:62F35 #msc:65K05 #msc:90C31 #msc:94B35 #stat.ML
paper · pdf · doi:10.48550/arxiv.1310.7637
openalex publication_date 2013/10/28 · arxiv created 2014/02/25 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study the robustness properties of ℓ1 norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the ℓ1 estimator for measurements errors consisting of outliers coupled with noise. We introduce a new estimation technique resulting from a regularization of ℓ1 minimization by inf-convolution with the ℓ2 norm. Concerning robustness to large outliers, the proposed estimator keeps the breakdown point of the ℓ1 estimator, and reduces to least squares when there are not outliers. We present a globally convergent forward-backward algorithm for computing our estimator and some numerical experiments confirming its theoretical properties.