Spectral algorithms in high dimensions exhibit a three-regime learning curve with benign overfitting in the under-regularized and interpolation regimes for source conditions 0 < s ≤ s*.
Optimal rates for the regularized least-squares algorithm
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Ridge regression in high dimensions exhibits power-law scalings because covariance fluctuations renormalize the ridge parameter, allowing closed-form error expressions and bias-variance decompositions for random feature models via free probability.
The paper derives sharp matching convergence rates for spectral methods in linear regression via feature space decomposition, enabling pre-ordering of algorithms and generalizing saturation effects.
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Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions
Spectral algorithms in high dimensions exhibit a three-regime learning curve with benign overfitting in the under-regularized and interpolation regimes for source conditions 0 < s ≤ s*.
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Scaling and renormalization in high-dimensional regression
Ridge regression in high dimensions exhibits power-law scalings because covariance fluctuations renormalize the ridge parameter, allowing closed-form error expressions and bias-variance decompositions for random feature models via free probability.
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Sharp convergence rates for Spectral methods via the feature space decomposition method
The paper derives sharp matching convergence rates for spectral methods in linear regression via feature space decomposition, enabling pre-ordering of algorithms and generalizing saturation effects.