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General nonexact oracle inequalities for classes with a subexponential envelope

Mendelson, Shahar; Lecué, Guillaume


We show that empirical risk minimization procedures and regularized empirical risk minimization procedures satisfy nonexact oracle inequalities in an unbounded framework, under the assumption that the class has a subexponential envelope function. The main novelty, in addition to the boundedness assumption free setup, is that those inequalities can yield fast rates even in situations in which exact oracle inequalities only hold with slower rates. We apply these results to show that...[Show more]

CollectionsANU Research Publications
Date published: 2012-04
Type: Journal article
Source: Annals of Statistics 40.2 (2012). 832-860
DOI: 10.1214/11-AOS965


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