Consistency of Interpolation with Laplace Kernels is a High-Dimensional Phenomenon
Machine Learning
2018-12-31 v1 Machine Learning
Statistics Theory
Statistics Theory
Abstract
We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected based on data. The result supports the empirical observation that minimum-norm interpolation (that is, exact fit to training data) in RKHS generalizes well for some high-dimensional datasets, but not for low-dimensional ones.
Keywords
Cite
@article{arxiv.1812.11167,
title = {Consistency of Interpolation with Laplace Kernels is a High-Dimensional Phenomenon},
author = {Alexander Rakhlin and Xiyu Zhai},
journal= {arXiv preprint arXiv:1812.11167},
year = {2018}
}