Computer Science > Machine Learning
[Submitted on 3 Jan 2024 (v1), last revised 16 Jul 2024 (this version, v2)]
Title:Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay
View PDF HTML (experimental)Abstract:The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice of the regularization parameter rather than the minimax rate. In this work, under mild assumptions, we rigorously provide a full characterization of the generalization error curves of the kernel gradient descent method (and a large class of analytic spectral algorithms) in kernel regression. Consequently, we could sharpen the near inconsistency of kernel interpolation and clarify the saturation effects of kernel regression algorithms with higher qualification, etc. Thanks to the neural tangent kernel theory, these results greatly improve our understanding of the generalization behavior of training the wide neural networks. A novel technical contribution, the analytic functional argument, might be of independent interest.
Submission history
From: Yicheng Li [view email][v1] Wed, 3 Jan 2024 08:00:50 UTC (203 KB)
[v2] Tue, 16 Jul 2024 01:15:57 UTC (93 KB)
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