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This research aims to improve the Lasso method's robustness against outliers and heavy-tailed noise using a novel exponential loss function.

Robust sparse penalization under heavy-tailed noise and outliers with exponential-type loss via the LASSO

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Randomized trial demonstrates improved variable selection in high-dimensional statistics, suggesting robustness against outliers.

This research aims to improve the Lasso method's robustness against outliers and heavy-tailed noise using a novel exponential loss function.
Integrates an exponential-type loss function within the Lasso framework.
Optimizes the estimator using a Majorization-Minimization (MM) algorithm.
Conducts numerical experiments comparing performance against the classical Lasso.
The proposed method achieves strong statistical convergence rates under heavy-tailed contamination.
Numerical experiments show the method outperforms classical Lasso in contaminated settings.
Maintains strong performance even under Gaussian noise conditions.

The Tien Mai (2026) studied this question.

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