ℓ₂-Boosting exhibits benign overfitting with logarithmic excess variance decay Θ(σ²/log(p/n)) under isotropic noise due to ℓ₁ bias, and a subdifferential early stopping rule recovers minimax-optimal ℓ₁ rates.
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Negative-capable ridge regression uses controlled negative regularization as anti-shrinkage to increase effective complexity along weak eigendirections and mitigate underfitting in small-data regression.
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When Does $\ell_2$-Boosting Overfit Benignly? High-Dimensional Risk Asymptotics and the $\ell_1$ Implicit Bias
ℓ₂-Boosting exhibits benign overfitting with logarithmic excess variance decay Θ(σ²/log(p/n)) under isotropic noise due to ℓ₁ bias, and a subdifferential early stopping rule recovers minimax-optimal ℓ₁ rates.
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A Ridge Too Far: Correcting Over-Shrinkage via Negative Regularization
Negative-capable ridge regression uses controlled negative regularization as anti-shrinkage to increase effective complexity along weak eigendirections and mitigate underfitting in small-data regression.