Optimal Oracle Inequality for Aggregation of Classifiers Under Low Noise Condition

  • Guillaume Lecué
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4005)


We consider the problem of optimality, in a minimax sense, and adaptivity to the margin and to regularity in binary classification. We prove an oracle inequality, under the margin assumption (low noise condition), satisfied by an aggregation procedure which uses exponential weights. This oracle inequality has an optimal residual: (logM/n) κ/(2κ− 1) where κ is the margin parameter, M the number of classifiers to aggregate and n the number of observations. We use this inequality first to construct minimax classifiers under margin and regularity assumptions and second to aggregate them to obtain a classifier which is adaptive both to the margin and regularity. Moreover, by aggregating plug-in classifiers (only logn), we provide an easily implementable classifier adaptive both to the margin and to regularity.


Support Vector Machine Optimal Rate Prediction Rule Empirical Risk Aggregation Procedure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Guillaume Lecué
    • 1
  1. 1.Laboratoire de Probabilités et Modèles Aléatoires (UMR CNRS 7599)Université Paris VIParisFrance

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