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- W3138817264 abstract "We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors converge as the number of parameters grows, and the limiting interpolant belongs to a reproducing kernel Hilbert space. This rigorously establishes an implicit bias of minimum weighted norm interpolation and explains why norm minimization may either benefit or suffer from over-parameterization. As special cases of this theory, we study interpolation by trigonometric polynomials and spherical harmonics. Our approach is from a deterministic and approximation theory viewpoint, as opposed to a statistical or random matrix one." @default.
- W3138817264 created "2021-03-29" @default.
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- W3138817264 date "2021-01-01" @default.
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- W3138817264 title "Generalization Error of Minimum Weighted Norm and Kernel Interpolation" @default.
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- W3138817264 doi "https://doi.org/10.1137/20m1359912" @default.
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