It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than n −1/2 . The work on this subject has suggested the following two conjectures: (i) the best achievable fast rate is of the order n −1 , and (ii) the plug-in classifiers generally converge more slowly than the classifiers based on empirical risk minimization. We show that both conjectures are not correct. In particular, we construct plug-in classifiers that can achieve not only fast, but also super-fast rates, that is, rates faster than n −1 . We establish minimax lower bounds showing that the obtained rates cannot be improved.
Firstly, it is based on plug-in classifier design REF , and not the standard empirical risk minimization (ERM) scheme.
Fast learning rates for plug-in classifiers
Annals of Statistics 2007, Vol. 35, No. 2, 608-633
Mathematics