Solving lp-norm regularization with tensor kernels

Saverio Salzo, Lorenzo Rosasco, Johan Suykens
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1655-1663, 2018.

Abstract

In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of lp regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast recent findings suggesting kernel methods cannot be extended beyond Hilbert setting. Numerical experiments confirm the effectiveness of the method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-salzo18a, title = {Solving lp-norm regularization with tensor kernels}, author = {Salzo, Saverio and Rosasco, Lorenzo and Suykens, Johan}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1655--1663}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/salzo18a/salzo18a.pdf}, url = {https://proceedings.mlr.press/v84/salzo18a.html}, abstract = {In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of lp regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast recent findings suggesting kernel methods cannot be extended beyond Hilbert setting. Numerical experiments confirm the effectiveness of the method. } }
Endnote
%0 Conference Paper %T Solving lp-norm regularization with tensor kernels %A Saverio Salzo %A Lorenzo Rosasco %A Johan Suykens %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-salzo18a %I PMLR %P 1655--1663 %U https://proceedings.mlr.press/v84/salzo18a.html %V 84 %X In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of lp regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast recent findings suggesting kernel methods cannot be extended beyond Hilbert setting. Numerical experiments confirm the effectiveness of the method.
APA
Salzo, S., Rosasco, L. & Suykens, J.. (2018). Solving lp-norm regularization with tensor kernels. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1655-1663 Available from https://proceedings.mlr.press/v84/salzo18a.html.

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