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.
Learning Bounds for Kernel Regression Using Eff ective Data Dimensionality
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New conditions for support vector proliferation (SVP) in RKHS for bounded orthonormal systems and sub-Gaussian features, yielding generalization bounds for kernel SVMs beyond prior restrictive assumptions.
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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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New Equivalences Between Interpolation and SVMs: Kernels and Structured Features
New conditions for support vector proliferation (SVP) in RKHS for bounded orthonormal systems and sub-Gaussian features, yielding generalization bounds for kernel SVMs beyond prior restrictive assumptions.