Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions
Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored. We study the learning curve and benign overfitting of spectral algorithms in the large-dimensional setting where the sample size and dimension are of comparable order, i.e., $n \asymp d^γ$ for some $γ>0$. We first consider inner-product kernels on the sphere $\mathbb{S}^{d-1}$ and establish a sharp asymptotic characterization of the excess risk across the full regularization path under various source conditions $s \geq 0$, where $s$ measures the relative smoothness of the regression function. Our results reveal ...
| Authors | Weihao Lu, Qian Lin, Yingcun Xia et al. |
|---|---|
| Primary category | stat.ML |
| Published | 25 April 2026 |
| Last updated at source | 25 April 2026 |
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