Simon Buchholz. Kernel interpolation in Sobolev spaces is not consistent in low dimensions. In Po-Ling Loh and Maxim Raginsky, editors, Proceedings of Thirty Fifth Conference on Learning Theory, volume 178 of Proceedings of Machine Learning Research, pages 3410-3440. PMLR, July 2022.
Andrea Caponnetto and Ernesto De Vito. Optimal rates for the regularized least-squares algorithm. Foundations of Computational Mathematics, 7(3):331-368, 2007. doi: 10.1007/s10208-006-0196-8.
Hugo Cui, Bruno Loureiro, Florent Krzakala, and Lenka Zdeborova. Generalization error rates in kernel regression: The crossover from the noiseless to noisy regime. Advances in Neural Information Processing Systems, 34:10131-10143, 2021.
Simon-Raphael Fischer and Ingo Steinwart. Sobolev norm learning rates for regularized least-squares algorithms. Journal of Machine Learning Research, 21:205:1-205:38, 2020.
Junichi Fujii, Masatoshi Fujii, Takayuki Furuta, and Ritsuo Nakamoto. Norm inequalities equivalent to Heinz inequality. Proceedings of the American Mathematical Society, 118(3):827-830, 1993.
Arthur Jacot, Franck Gabriel, and Clement Hongler. Neural tangent kernel: Convergence and generalization in neural networks. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018.
Arthur Jacot, Berfin Şimşek, Francesco Spadaro, Clément Hongler, and Franck Gabriel. Kernel alignment risk estimator: Risk prediction from training data. June 2020. doi: 10.48550/arXiv.2006.09796.
Hui Jin, Pradeep Kr Banerjee, and Guido Montúfar. Learning curves for Gaussian process regression with power-law priors and targets. (arXiv:2110.12231), November 2021.
Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic, and Bharath K. Sriperumbudur. Gaussian processes and kernel methods: A review on connections and equivalences. arXiv preprint arXiv:1807.02582, 2018.
Jianfa Lai, Manyun Xu, Rui Chen, and Qian Lin. Generalization ability of wide neural networks on R. (arXiv:2302.05933), February 2023. doi: 10.48550/arXiv.2302.05933.
Yicheng Li, Haobo Zhang, and Qian Lin. Kernel interpolation generalizes poorly. (arXiv:2303.15809), March 2023a. doi: 10.48550/arXiv.2303.15809.
Yicheng Li, Haobo Zhang, and Qian Lin. On the saturation effect of kernel ridge regression. In International Conference on Learning Representations, February 2023b.
Tengyuan Liang and Alexander Rakhlin. Just interpolate: Kernel "ridgeless" regression can generalize. The Annals of Statistics, 48(3), June 2020. ISSN 0090-5364. doi: 10.1214/19-AOS1849.
Junhong Lin, Alessandro Rudi, L. Rosasco, and V. Cevher. Optimal rates for spectral algorithms with least-squares regression over Hilbert spaces. Applied and Computational Harmonic Analysis, 48: 868-890, 2018. doi: 10.1016/j.acha.2018.09.009.
Shao-Bo Lin, Xiangyu Chang, and Xingping Sun. Kernel interpolation of high dimensional scattered data. (arXiv:2009.01514), September 2021.
Neil Mallinar, James B. Simon, Amirhesam Abedsoltan, Parthe Pandit, Mikhail Belkin, and Preetum Nakkiran. Benign, tempered, or catastrophic: A taxonomy of overfitting. (arXiv:2207.06569), July 2022. doi: 10.48550/arXiv.2207.06569.
Charles A. Micchelli and Grace Wahba. Design problems for optimal surface interpolation. Technical report, Wisconsin Univ-Madison Dept of Statistics, 1979.
Alexander Rakhlin and Xiyu Zhai. Consistency of interpolation with Laplace kernels is a high-dimensional phenomenon. (arXiv:1812.11167), December 2018.