A Moment Bound for Multi-hinge Classifiers

Bernadetta Tarigan, Sara A. van de Geer.

Year: 2008, Volume: 9, Issue: 71, Pages: 2171−2185


The success of support vector machines in binary classification relies on the fact that hinge loss employed in the risk minimization targets the Bayes rule. Recent research explores some extensions of this large margin based method to the multicategory case. We show a moment bound for the so-called multi-hinge loss minimizers based on two kinds of complexity constraints: entropy with bracketing and empirical entropy. Obtaining such a result based on the latter is harder than finding one based on the former. We obtain fast rates of convergence that adapt to the unknown margin.