PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Fast learning rates for plug-in classifiers
Jean-Yves Audibert and Alexandre Tsybakov
The Annals of Statistics Volume 35, Number 2, pp. 608-633, 2007.

Abstract

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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3152
Deposited By:Jean-Yves Audibert
Deposited On:29 December 2007