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Aggregation procedures: optimality and fast rates

Abstract : In this thesis we deal with aggregation
procedures under the margin assumption. We prove that the margin
assumption improves the rate of aggregation. Another contribution of
this thesis is to show that some empirical risk minimization
procedures are suboptimal when the loss function is convex, even
under the margin assumption. Contrarily to some aggregation
procedures with exponential weights, these model selection methods
cannot benefit from the large margin. Then, we apply aggregation
methods to construct adaptive estimators in several different
problems. The final contribution of this thesis is to purpose a new
approach to the control of the bias term in classification by
introducing some spaces of sparse prediction rules. Minimax rates of
convergence have been obtained for these classes of functions and,
by using an aggregation method, we provide an adaptive version of
these estimators.
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Contributor : Guillaume Lecué <>
Submitted on : Wednesday, May 30, 2007 - 1:00:13 PM
Last modification on : Wednesday, December 9, 2020 - 3:05:59 PM
Long-term archiving on: : Thursday, April 8, 2010 - 6:23:20 PM


  • HAL Id : tel-00150402, version 1


Guillaume Lecué. Aggregation procedures: optimality and fast rates. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2007. English. ⟨tel-00150402⟩



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