Sample Complexity of Classifiers Taking Values in R^Q, Application to Multi-Class SVMs ## AbstractBounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such "VC dimensions" exist for models taking values in {0, 1}, {1, ..., Q} and R. We introduce the generalizations appropriate for the missing case, the one of models with values in R^Q. This provides us with a new guaranteed risk for M-SVMs. For those models, a sharper bound is obtained by using the Rademacher complexity.
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