Learning between the peaks: sharp asymptotics for kernel ridge regression under power-law anisotropy
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 anisotropy ($0<α<1$), the problem remains effectively high-dimensional and retains some features of the isotropic case, while departing from it in others: the variance still peaks at integer sample complexities $κ\in\mathbb{N}$, but these peaks are progressively damped as $α$ grows; meanwhile, for targets...
| Authors | Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro |
|---|---|
| Primary category | stat.ML |
| Published | 28 August 2026 |
| Last updated at source | 28 August 2026 |
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