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• W2950382171 abstract "In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for empirical multi-class risk minimization algorithms using an arbitrary norm as regularizer. Key to our analysis are new structural results for multi-class Gaussian complexities and empirical $ell_infty$-norm covering numbers, which exploit the Lipschitz continuity of the loss function with respect to the $ell_2$- and $ell_infty$-norm, respectively. We establish data-dependent error bounds in terms of complexities of a linear function class defined on a finite set induced by training examples, for which we show tight lower and upper bounds. We apply the results to several prominent multi-class learning machines, exhibiting a tighter dependency on the number of classes than the state of the art. For instance, for the multi-class SVM by Crammer and Singer (2002), we obtain a data-dependent bound with a logarithmic dependency which significantly improves the previous square-root dependency. Experimental results are reported to verify the effectiveness of our theoretical findings." @default.
• W2950382171 created "2019-06-27" @default.
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• W2950382171 date "2017-06-29" @default.
• W2950382171 modified "2023-09-26" @default.
• W2950382171 title "Data-dependent Generalization Bounds for Multi-class Classification" @default.
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• W2950382171 doi "https://doi.org/10.48550/arxiv.1706.09814" @default.
• W2950382171 hasPublicationYear "2017" @default.
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