Outlier Robust and Sparse Estimation of Linear Regression Coefficients

2022/08/24 by Sasai, Takeyuki, Fujisawa, Hironori · 1 citation
#62F35 #62J07 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2208.11592

Abstract

We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present sharper error bounds under weaker assumptions than prior studies that share similar interests with this study. Our analysis relies on some sharp concentration inequalities resulting from generic chaining.

Cited by

• Non-Asymptotic Analysis of Efficiency in Conformalized Regression

Related

• Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates
• Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliers
• Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties
• Outlier-robust Estimation of a Sparse Linear Model Using Invexity
• Heavy-tailed Contamination is Easier than Adversarial Contamination