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# Title: L p -norm Sauer-Shelah Lemma for Margin Multi-category Classifiers

Authors: Yann Guermeur (ABC)
Abstract: In the framework of agnostic learning, one of the main open problems of the theory of multi-category pattern classification is the characterization of the way the complexity varies with the number C of categories. More precisely, if the classifier is characterized only through minimal learnability hypotheses, then the optimal dependency on C that an upper bound on the probability of error should exhibit is unknown. We consider margin classifiers. They are based on classes of vector-valued functions with one component function per category, and the classes of component functions are uniform Glivenko-Cantelli classes. For these classifiers, an L p-norm Sauer-Shelah lemma is established. It is then used to derive guaranteed risks in the L $\infty$ and L 2-norms. These bounds improve over the state-of-the-art ones with respect to their dependency on C, which is sublinear.
 Subjects: Statistics Theory (math.ST) Cite as: arXiv:1609.07953 [math.ST] (or arXiv:1609.07953v1 [math.ST] for this version)

## Submission history

From: Yann Guermeur [view email]
[v1] Mon, 26 Sep 2016 12:49:07 GMT (27kb,D)