2004/08/01 by Gábor Lugosi, Gabor Lugosi, Marten Wegkamp · 1 citation
Computer Science · Mathematics · #Face and Expression Recognition #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques #math.ST #msc:60E15. #msc:62G99 #msc:62H30 #stat.TH
paper · pdf · doi:10.1214/009053604000000463
published as Annals of Statistics 2004, Vol. 32, No. 4, 1679-1697 · 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
openalex publication_date 2004/08/01 · arxiv created 2004/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.