How rotational invariance of common kernels prevents generalization in high dimensions
Konstantin Donhauser,
Mingqi Wu,
Fanny Yang
Abstract:Kernel ridge regression is well-known to achieve minimax optimal rates in low-dimensional settings. However, its behavior in high dimensions is much less understood. Recent work establishes consistency for kernel regression under certain assumptions on the ground truth function and the distribution of the input data. In this paper, we show that the rotational invariance property of commonly studied kernels (such as RBF, inner product kernels and fully-connected NTK of any depth) induces a bias towards low-degr… Show more
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