Kernel interpolation in Sobolev spaces is not consistent in low dimensions
Abstract
We consider kernel ridgeless ridge regression with kernels whose associated RKHS is a Sobolev space $H^s$. We show for $d/2 Cite this Paper BibTeX @InProceedings{pmlr-v178-buchholz22a, title = {Kernel interpolation in Sobolev spaces is not consistent in low dimensions}, author = {Buchholz, Simon}, booktitle = {Proceedings of Thirty Fifth Conference on Learning Theory}, pages = {3410--3440}, year = {2022}, editor = {Loh, Po-Ling and Raginsky, Maxim}, volume = {178}, series = {Proceedings of Machine Learning Research}, month = {02--05 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v178/buchholz22a/buchholz22a.pdf}, url = {https://proceedings.mlr.press/v178/buchholz22a.html}, abstract = {We consider kernel ridgeless ridge regression with kernels whose associated RKHS is a Sobolev space $H^s$. We show for $d/2 Copy to Clipboard Download Endnote %0 Conference Paper %T Kernel interpolation in Sobolev spaces is not consistent in low dimensions %A Simon Buchholz %B Proceedings of Thirty Fifth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2022 %E Po-Ling Loh %E Maxim Raginsky %F pmlr-v178-buchholz22a %I PMLR %P 3410--3440 %U https://proceedings.mlr.press/v178/buchholz22a.html %V 178 %X We consider kernel ridgeless ridge regression with kernels whose associated RKHS is a Sobolev space $H^s$. We show for $d/2 Copy to Clipboard Download APA Buchholz, S.. (2022). Kernel interpolation in Sobolev spaces is not consistent in low dimensions. Proceedings of Thirty Fifth Conference on Learning Theory, in Proceedings of Machine Learning Research 178:3410-3440 Available from https://proceedings.mlr.press/v178/buchholz22a.html. Copy to Clipboard Download Related Material Download PDF