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| Detailed view | Preprint, Working Paper, ... |
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| Available versions: | v1 (2005-07-08) | v2 (2005-09-13) | v3 (2011-05-27) |
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| Fast learning rates for plug-in classifiers under the margin condition |
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| Jean-Yves Audibert1Alexandre B. Tsybakov2 |
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| 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, i.e., the rates faster than $n^{-1/2}$. The works on this subject 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 slower 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 the fast, but also the {\it super-fast} rates, i.e., the rates faster than $n^{-1}$. We establish minimax lower bounds showing that the obtained rates cannot be improved. |
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| 1: | CERTIS - Centre d'Enseignement et de Recherche en Technologies de l'Information et Systèmes |
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| 2: | LPMA - Laboratoire de Probabilités et Modèles Aléatoires |
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| classification – statistical learning – fast rates of convergence – excess risk – plug-in classifiers – minimax lower bounds |
| hal-00005882, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00005882 | |
| oai:hal.archives-ouvertes.fr:hal-00005882 | |
| From: Jean-Yves Audibert | |
| Submitted on: Tuesday, 24 May 2011 10:31:16 | |
| Updated on: Thursday, 9 June 2011 10:34:14 | |
