Local Rademacher complexities and oracle inequalities in risk minimization
نویسندگان
چکیده
منابع مشابه
Discussion: Local Rademacher Complexities and Oracle Inequalities in Risk Minimization
In this magnificent paper, Professor Koltchinskii offers general and powerful performance bounds for empirical risk minimization, a fundamental principle of statistical learning theory. Since the elegant pioneering work of Vapnik and Chervonenkis in the early 1970s, various such bounds have been known that relate the performance of empirical risk minimizers to combinatorial and geometrical feat...
متن کاملRejoinder: 2004 Ims Medallion Lecture: Local Rademacher Complexities and Oracle Inequalities in Risk Minimization
of the true risk function F ∋ f 7→ Pf. The first quantity of interest is the L2-diameter of this set, D(F ; δ), and the second one is the function φn(F ; δ) that is equal to the expected supremum of empirical process indexed by the differences f − g, f, g ∈F(δ). These two functions are then combined in the expression Ūn(δ; t) that has its roots in Talagrand’s concentration inequalities for empi...
متن کاملMedallion Lecture Local Rademacher Complexities and Oracle Inequalities in Risk Minimization
Let F be a class of measurable functions f :S 7→ [0,1] defined on a probability space (S,A, P ). Given a sample (X1, . . . ,Xn) of i.i.d. random variables taking values in S with common distribution P , let Pn denote the empirical measure based on (X1, . . . ,Xn). We study an empirical risk minimization problem Pnf →min, f ∈ F . Given a solution f̂n of this problem, the goal is to obtain very ge...
متن کاملDiscussion of “2004 Ims Medallion Lecture: Local Rademacher Complexities and Oracle Inequalities in Risk Minimization” by v. Koltchinskii
These last years, much attention has been paid to the construction of model selection criteria via penalization. Vladimir Koltchinskii has to be congratulated for providing a theory reaching a level of generality that is sufficiently high to recover most of the recent results obtained on this topic in the context of statistical learning. Thanks to concentration inequalities and empirical proces...
متن کاملDiscussion of “2004 Ims Medallion Lecture: Local Rademacher Complexities and Oracle Inequalities in Risk Minimization” by v. Koltchinskii
1. Introduction. This paper unifies and extends important theoretical results on empirical risk minimization and model selection. It makes extensive and efficient use of new probability inequalities for the amount of concentration of the (possibly symmetrized) empirical process around its mean. The results are very subtle and very pleasing indeed, as they show that oracle inequalities exist for...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2006
ISSN: 0090-5364
DOI: 10.1214/009053606000001019