PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Margin adaptive model selection in statistical learning
Sylvain Arlot and Peter L. Bartlett
Bernoulli Volume 17, Number 2, pp. 687-713, 2008. ISSN 1350-7265


A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning framework. Actually, we consider a weaker version of this condition that allows one to take into account that learning within a small model can be much easier than within a large one. Requiring this “strong margin adaptivity” makes the model selection problem more challenging. We first prove, in a general framework, that some penalization procedures (including local Rademacher complexities) exhibit this adaptivity when the models are nested. Contrary to previous results, this holds with penalties that only depend on the data. Our second main result is that strong margin adaptivity is not always possible when the models are not nested: for every model selection procedure (even a randomized one), there is a problem for which it does not demonstrate strong margin adaptivity.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:4547
Deposited By:Sylvain Arlot
Deposited On:13 March 2009