A Note on Extending Generalization Bounds for Binary Large-Margin Classifiers to Multiple Classes

Ürün Dogan, Tobias Glasmachers, Christian Igel

Abstract: A generic way to extend generalization bounds for binary large-margin classifiers to large-margin multi-category classifiers is presented. The simple proceeding leads to surprisingly tight bounds showing the same \(\tilde{O}(d^2)\) scaling in the number d of classes as state-of-the-art results. The approach is exemplified by extending a textbook bound based on Rademacher complexity, which leads to a multi-class bound depending on the sum of the margin violations of the classifier.