Complexity regularization via localized random penalties

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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.
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/009053604000000463

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Statistics Theory, 62H30, 62G99 (Primary) 60E15. (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/130637

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410091
 http://arxiv.org/abs/math/0410091
 Annals of Statistics 2004, Vol. 32, No. 4, 1679-1697
 doi:10.1214/009053604000000463

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arXiv