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

Takeyuki Sasai; Hironori Fujisawa

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arXiv · 2408.01336

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

Takeyuki Sasai·Hironori Fujisawa

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Abstract

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.

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Takeyuki Sasai, Hironori Fujisawa. 2024-08-02. Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliers. https://arxiv.org/abs/2408.01336

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