Complexity regularization via localized random penalties

Details Complexity regularization via localized random penalties Complexity regularization via localized random penalties

2004-10-05

arxiv.org/abs/math/0410091v1

Annals of Statistics 2004, Vol. 32, No. 4, 1679-1697

Mathematics

Statistics Theory

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat

Scientific paper

10.1214/009053604000000463

In this article, model selection via penalized empirical loss minimization in nonparametric classification problems is studied. Data-dependent penalties are constructed, which are based on estimates of the complexity of a small subclass of each model class, containing only those functions with small empirical loss. The penalties are novel since those considered in the literature are typically based on the entire model class. Oracle inequalities using these penalties are established, and the advantage of the new penalties over those based on the complexity of the whole model class is demonstrated.

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