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.
Generalization in kernel regression under realistic assumptions
4 Pith papers cite this work. Polarity classification is still indexing.
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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.
Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).
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.