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Summary: Fast learning rates for plug-in classifiers
under the margin condition
Jean-Yves AUDIBERT1
and Alexandre B. TSYBAKOV2
1
Ecole Nationale des Ponts et Chauss´ees, 2
Universit´e Pierre et Marie Curie
May 10, 2011
Abstract
It has been recently shown that, under the margin (or low noise) assump-
tion, there exist classifiers attaining fast rates of convergence of the excess
Bayes risk, i.e., the rates faster than n-1/2. The works on this subject sug-
gested the following two conjectures: (i) the best achievable fast rate is of the
order n-1, and (ii) the plug-in classifiers generally converge slower than the
classifiers based on empirical risk minimization. We show that both conjec-
tures are not correct. In particular, we construct plug-in classifiers that can
achieve not only the fast, but also the super-fast rates, i.e., the rates faster
than n-1. We establish minimax lower bounds showing that the obtained
rates cannot be improved.
AMS 2000 Subject classifications. Primary 62G07, Secondary 62G08, 62H05,
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