The impact of contamination and correlated design on the Lasso: An average case analysis

Stanislav Minsker and Yiqiu Shen

Statistics & Probability Letters, 2025, vol. 223, issue C

Abstract: We study the prediction problem in the context of the high-dimensional linear regression model. We focus on the practically relevant framework where a fraction of the linear measurements is corrupted while the columns of the design matrix can be moderately correlated. Our findings suggest that for most sparse signals, the Lasso estimator admits strong performance guarantees under more easily verifiable and less stringent assumptions on the design matrix compared to much of the existing literature.

Keywords: Lasso; Incoherence; Robustness; Norms of random submatrices (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110417

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