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.
citing papers explorer
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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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Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces
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)).
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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.