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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Separability of high-dimensional matrix covariances can be tested by Monte Carlo sphericity after separable MLE whitening, with an angular version robust to heavy-tailed elliptical laws and consistency under dense alternatives.
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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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Testing Covariance Separability in High Dimensions
Separability of high-dimensional matrix covariances can be tested by Monte Carlo sphericity after separable MLE whitening, with an angular version robust to heavy-tailed elliptical laws and consistency under dense alternatives.