2022-06-28-buchholz22a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Kernel interpolation in Sobolev spaces is not consistent in low dimensions	We consider kernel ridgeless ridge regression with kernels whose associated RKHS is a Sobolev space $H^s$. We show for $d/2<s<3d/4$ that interpolation is not consistent in fixed dimension extending earlier results for the Laplace kernel in odd dimensions and underlining again that benign overfitting is rare in low dimensions. The proof proceeds by deriving sharp bounds on the spectrum of random kernel matrices using results from the theory of radial basis functions which might be of independent interest.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	buchholz22a	0	Kernel interpolation in Sobolev spaces is not consistent in low dimensions	3410	3440	3410-3440	3410	false	Buchholz, Simon	given family Simon Buchholz	2022-06-28		Proceedings of Thirty Fifth Conference on Learning Theory	178	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v178/buchholz22a/buchholz22a.pdf