Relative Deviation Margin Bounds

Corinna Cortes, Mehryar Mohri, Ananda Theertha Suresh
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:2122-2131, 2021.

Abstract

We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. e give two types of learning bounds, in terms of either the Rademacher complexity or the empirical $\ell_\infty$-covering number of the hypothesis set used, both distribution-dependent and valid for general families. Furthermore, using our relative deviation margin bounds, we derive distribution-dependent generalization bounds for unbounded loss functions under the assumption of a finite moment. We also briefly highlight several applications of these bounds and discuss their connection with existing results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-cortes21a, title = {Relative Deviation Margin Bounds}, author = {Cortes, Corinna and Mohri, Mehryar and Suresh, Ananda Theertha}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {2122--2131}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/cortes21a/cortes21a.pdf}, url = {https://proceedings.mlr.press/v139/cortes21a.html}, abstract = {We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. e give two types of learning bounds, in terms of either the Rademacher complexity or the empirical $\ell_\infty$-covering number of the hypothesis set used, both distribution-dependent and valid for general families. Furthermore, using our relative deviation margin bounds, we derive distribution-dependent generalization bounds for unbounded loss functions under the assumption of a finite moment. We also briefly highlight several applications of these bounds and discuss their connection with existing results.} }
Endnote
%0 Conference Paper %T Relative Deviation Margin Bounds %A Corinna Cortes %A Mehryar Mohri %A Ananda Theertha Suresh %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-cortes21a %I PMLR %P 2122--2131 %U https://proceedings.mlr.press/v139/cortes21a.html %V 139 %X We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. e give two types of learning bounds, in terms of either the Rademacher complexity or the empirical $\ell_\infty$-covering number of the hypothesis set used, both distribution-dependent and valid for general families. Furthermore, using our relative deviation margin bounds, we derive distribution-dependent generalization bounds for unbounded loss functions under the assumption of a finite moment. We also briefly highlight several applications of these bounds and discuss their connection with existing results.
APA
Cortes, C., Mohri, M. & Suresh, A.T.. (2021). Relative Deviation Margin Bounds. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:2122-2131 Available from https://proceedings.mlr.press/v139/cortes21a.html.

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