On the Consistency of Max-Margin Losses

Alex Nowak, Alessandro Rudi, Francis Bach
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:4612-4633, 2022.

Abstract

The foundational concept of Max-Margin in machine learning is ill-posed for output spaces with more than two labels such as in structured prediction. In this paper, we show that the Max-Margin loss can only be consistent to the classification task under highly restrictive assumptions on the discrete loss measuring the error between outputs. These conditions are satisfied by distances defined in tree graphs, for which we prove consistency, thus being the first losses shown to be consistent for Max-Margin beyond the binary setting. We finally address these limitations by correcting the concept of Max-Margin and introducing the Restricted-Max-Margin, where the maximization of the loss-augmented scores is maintained, but performed over a subset of the original domain. The resulting loss is also a generalization of the binary support vector machine and it is consistent under milder conditions on the discrete loss.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-nowak22a, title = { On the Consistency of Max-Margin Losses }, author = {Nowak, Alex and Rudi, Alessandro and Bach, Francis}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {4612--4633}, 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/nowak22a/nowak22a.pdf}, url = {https://proceedings.mlr.press/v151/nowak22a.html}, abstract = { The foundational concept of Max-Margin in machine learning is ill-posed for output spaces with more than two labels such as in structured prediction. In this paper, we show that the Max-Margin loss can only be consistent to the classification task under highly restrictive assumptions on the discrete loss measuring the error between outputs. These conditions are satisfied by distances defined in tree graphs, for which we prove consistency, thus being the first losses shown to be consistent for Max-Margin beyond the binary setting. We finally address these limitations by correcting the concept of Max-Margin and introducing the Restricted-Max-Margin, where the maximization of the loss-augmented scores is maintained, but performed over a subset of the original domain. The resulting loss is also a generalization of the binary support vector machine and it is consistent under milder conditions on the discrete loss. } }
Endnote
%0 Conference Paper %T On the Consistency of Max-Margin Losses %A Alex Nowak %A Alessandro Rudi %A Francis Bach %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-nowak22a %I PMLR %P 4612--4633 %U https://proceedings.mlr.press/v151/nowak22a.html %V 151 %X The foundational concept of Max-Margin in machine learning is ill-posed for output spaces with more than two labels such as in structured prediction. In this paper, we show that the Max-Margin loss can only be consistent to the classification task under highly restrictive assumptions on the discrete loss measuring the error between outputs. These conditions are satisfied by distances defined in tree graphs, for which we prove consistency, thus being the first losses shown to be consistent for Max-Margin beyond the binary setting. We finally address these limitations by correcting the concept of Max-Margin and introducing the Restricted-Max-Margin, where the maximization of the loss-augmented scores is maintained, but performed over a subset of the original domain. The resulting loss is also a generalization of the binary support vector machine and it is consistent under milder conditions on the discrete loss.
APA
Nowak, A., Rudi, A. & Bach, F.. (2022). On the Consistency of Max-Margin Losses . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:4612-4633 Available from https://proceedings.mlr.press/v151/nowak22a.html.

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