Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum

• URL: http://arxiv.org/abs/2402.01297v3
• Date: Wed, 29 May 2024 19:23:41 GMT
• Title: Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum
• Authors: Tin Sum Cheng, Aurelien Lucchi, Anastasis Kratsios, David Belius,
• Abstract summary: We prove the phenomena of tempered overfitting and catastrophic overfitting under the sub-Gaussian design assumption. We also identify that the independence of the features plays an important role in guaranteeing tempered overfitting.
• Score: 6.749750044497731
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For kernels with polynomial spectral decay, we recover the bound from previous work; for exponential decay, our bound is non-trivial and novel. Our contribution is two-fold: (i) we rigorously prove the phenomena of tempered overfitting and catastrophic overfitting under the sub-Gaussian design assumption, closing an existing gap in the literature; (ii) we identify that the independence of the features plays an important role in guaranteeing tempered overfitting, raising concerns about approximating KRR generalization using the Gaussian design assumption in previous literature.

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