The paper proves high-probability, non-asymptotic bounds showing that kernel ridge regression and two-layer ReLU networks in the NTK regime can achieve both arbitrarily small training and test error without assuming the regression function lies in the kernel RKHS.
Regularised Least-Squares Regression with Infinite-Dimensional Output Space
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abstract
This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly infinite-dimensional) Hilbert space. Our approach is based on the integral operator technique using spectral theory for non-compact operators. We place a particular emphasis on obtaining results with as few assumptions as possible; as such we only use Chebyshev's inequality, and no effort is made to obtain the best rates or constants.
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cs.LG 1years
2025 1verdicts
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A Classical View on Benign Overfitting: The Role of Sample Size
The paper proves high-probability, non-asymptotic bounds showing that kernel ridge regression and two-layer ReLU networks in the NTK regime can achieve both arbitrarily small training and test error without assuming the regression function lies in the kernel RKHS.