Learning between the peaks: sharp asymptotics for kernel ridge regression under power-law anisotropy

Paper recorded by Signals 4 on 2026-08-28 in cs.LG. Abstract reproduced from arXiv; link to the original below.

Published 2026-08-28 on arXiv · recorded by Signals 4 on 2026-08-31

Category: cs.LG · 机器学习 · first seen 2026-08-31

Abstract

We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $α\geq 0$ for polynomial inner-product kernels. We derive asymptotically sharp expressions for the kernel spectrum and the generalization error in the polynomial high-dimensional regime $n=Θ(d^κ)$, revealing how anisotropy reshapes the learning curves. For weak anisotrop

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