Efficient Hyperparameter Tuning for Large Scale Kernel Ridge Regression

Giacomo Meanti, Luigi Carratino, Ernesto De Vito, Lorenzo Rosasco
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6554-6572, 2022.

Abstract

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming of these solutions is that hyperparameter tuning is not taken care of, and left for the user to perform. Hyperparameters are crucial in practice and the lack of automated tuning greatly hinders efficiency and usability. In this paper, we work to fill in this gap focusing on kernel ridge regression based on the Nyström approximation. After reviewing and contrasting a number of hyperparameter tuning strategies, we propose a complexity regularization criterion based on a data dependent penalty, and discuss its efficient optimization. Then, we proceed to a careful and extensive empirical evaluation highlighting strengths and weaknesses of the different tuning strategies. Our analysis shows the benefit of the proposed approach, that we hence incorporate in a library for large scale kernel methods to derive adaptively tuned solutions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-meanti22a, title = { Efficient Hyperparameter Tuning for Large Scale Kernel Ridge Regression }, author = {Meanti, Giacomo and Carratino, Luigi and De Vito, Ernesto and Rosasco, Lorenzo}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6554--6572}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/meanti22a/meanti22a.pdf}, url = {https://proceedings.mlr.press/v151/meanti22a.html}, abstract = { Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming of these solutions is that hyperparameter tuning is not taken care of, and left for the user to perform. Hyperparameters are crucial in practice and the lack of automated tuning greatly hinders efficiency and usability. In this paper, we work to fill in this gap focusing on kernel ridge regression based on the Nyström approximation. After reviewing and contrasting a number of hyperparameter tuning strategies, we propose a complexity regularization criterion based on a data dependent penalty, and discuss its efficient optimization. Then, we proceed to a careful and extensive empirical evaluation highlighting strengths and weaknesses of the different tuning strategies. Our analysis shows the benefit of the proposed approach, that we hence incorporate in a library for large scale kernel methods to derive adaptively tuned solutions. } }
Endnote
%0 Conference Paper %T Efficient Hyperparameter Tuning for Large Scale Kernel Ridge Regression %A Giacomo Meanti %A Luigi Carratino %A Ernesto De Vito %A Lorenzo Rosasco %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-meanti22a %I PMLR %P 6554--6572 %U https://proceedings.mlr.press/v151/meanti22a.html %V 151 %X Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming of these solutions is that hyperparameter tuning is not taken care of, and left for the user to perform. Hyperparameters are crucial in practice and the lack of automated tuning greatly hinders efficiency and usability. In this paper, we work to fill in this gap focusing on kernel ridge regression based on the Nyström approximation. After reviewing and contrasting a number of hyperparameter tuning strategies, we propose a complexity regularization criterion based on a data dependent penalty, and discuss its efficient optimization. Then, we proceed to a careful and extensive empirical evaluation highlighting strengths and weaknesses of the different tuning strategies. Our analysis shows the benefit of the proposed approach, that we hence incorporate in a library for large scale kernel methods to derive adaptively tuned solutions.
APA
Meanti, G., Carratino, L., De Vito, E. & Rosasco, L.. (2022). Efficient Hyperparameter Tuning for Large Scale Kernel Ridge Regression . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6554-6572 Available from https://proceedings.mlr.press/v151/meanti22a.html.

Related Material