Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum
- Cheng, Tin Sum
- Lucchi, Aurelien
- Kratsios, Anastasis
- Belius, David ORCID UniDistance Suisse
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2024
Published in:
- International Conference on Machine Learning (ICML) 2024. - 2024
English
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.
- Identifiers
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- DOI 10.48550/ARXIV.2402.01297
- URI https://pub.orcid.org/v3.0/0000-0003-3706-043X/work/207848311
- ARK ark:/51647/srd1336035
- Persistent URL
- https://n2t.net/ark:/51647/srd1336035
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