Multiclass learning with margin: exponential rates with no bias-variance trade-off

Stefano Vigogna, Giacomo Meanti, Ernesto De Vito, Lorenzo Rosasco
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:22260-22269, 2022.

Abstract

We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without any bias-variance trade-off. Different convergence rates can be obtained in correspondence of different margin assumptions. With a self-contained and instructive analysis we are able to generalize known results from the binary to the multiclass setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-vigogna22a, title = {Multiclass learning with margin: exponential rates with no bias-variance trade-off}, author = {Vigogna, Stefano and Meanti, Giacomo and De Vito, Ernesto and Rosasco, Lorenzo}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {22260--22269}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/vigogna22a/vigogna22a.pdf}, url = {https://proceedings.mlr.press/v162/vigogna22a.html}, abstract = {We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without any bias-variance trade-off. Different convergence rates can be obtained in correspondence of different margin assumptions. With a self-contained and instructive analysis we are able to generalize known results from the binary to the multiclass setting.} }
Endnote
%0 Conference Paper %T Multiclass learning with margin: exponential rates with no bias-variance trade-off %A Stefano Vigogna %A Giacomo Meanti %A Ernesto De Vito %A Lorenzo Rosasco %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-vigogna22a %I PMLR %P 22260--22269 %U https://proceedings.mlr.press/v162/vigogna22a.html %V 162 %X We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without any bias-variance trade-off. Different convergence rates can be obtained in correspondence of different margin assumptions. With a self-contained and instructive analysis we are able to generalize known results from the binary to the multiclass setting.
APA
Vigogna, S., Meanti, G., De Vito, E. & Rosasco, L.. (2022). Multiclass learning with margin: exponential rates with no bias-variance trade-off. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:22260-22269 Available from https://proceedings.mlr.press/v162/vigogna22a.html.

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