Uniform concentration and symmetrization for weak interactions

Andreas Maurer, Massimiliano Pontil
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:2372-2387, 2019.

Abstract

The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v99-maurer19a, title = {Uniform concentration and symmetrization for weak interactions}, author = {Maurer, Andreas and Pontil, Massimiliano}, booktitle = {Proceedings of the Thirty-Second Conference on Learning Theory}, pages = {2372--2387}, year = {2019}, editor = {Beygelzimer, Alina and Hsu, Daniel}, volume = {99}, series = {Proceedings of Machine Learning Research}, month = {25--28 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v99/maurer19a/maurer19a.pdf}, url = {https://proceedings.mlr.press/v99/maurer19a.html}, abstract = {The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.} }
Endnote
%0 Conference Paper %T Uniform concentration and symmetrization for weak interactions %A Andreas Maurer %A Massimiliano Pontil %B Proceedings of the Thirty-Second Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2019 %E Alina Beygelzimer %E Daniel Hsu %F pmlr-v99-maurer19a %I PMLR %P 2372--2387 %U https://proceedings.mlr.press/v99/maurer19a.html %V 99 %X The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.
APA
Maurer, A. & Pontil, M.. (2019). Uniform concentration and symmetrization for weak interactions. Proceedings of the Thirty-Second Conference on Learning Theory, in Proceedings of Machine Learning Research 99:2372-2387 Available from https://proceedings.mlr.press/v99/maurer19a.html.

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