Optimal rates of aggregation in classification under low noise assumption

Abstract

In the same spirit as Tsybakov (2003), we define the optimality of an aggregation procedure in the problem of classification. Using an aggregate with exponential weights, we obtain an optimal rate of convex aggregation for the hinge risk under the margin assumption. Moreover we obtain an optimal rate of model selection aggregation under the margin assumption for the excess Bayes risk.

References in corpus (7)

• Fast learning rates for plug-in classifiers
• Fast rates for support vector machines using Gaussian kernels
• Risk bounds for statistical learning
• Aggregation for Gaussian regression
• Statistical performance of support vector machines
• Learning by mirror averaging
• Simultaneous adaptation to the margin and to complexity in classification

Cited by in corpus (4)

• Fast learning rates in statistical inference through aggregation
• Mirror averaging with sparsity priors
• Optimal learning with $Q$-aggregation
• An adaptive multiclass nearest neighbor classifier