Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
32 [LS24] Guillaume Lecu´ e and Zong Shang
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Introduces alignment-sensitive effective span dimension (ESD) for learned-kernel spectral algorithms and proves minimax excess risk bounds of order sigma^2 * ESD, with gradient flow shown to reduce ESD.
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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Large Dimensional Kernel Ridge Regression: Extending to Product Kernels
Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
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Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels
Introduces alignment-sensitive effective span dimension (ESD) for learned-kernel spectral algorithms and proves minimax excess risk bounds of order sigma^2 * ESD, with gradient flow shown to reduce ESD.
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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.