Concentration Inequalities and Model Selection: Ecole D'Eté de Probabilités de Saint-Flour XXXIII - 2003
Concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn to be essential tools to develop a non asymptotic theory in statistics. This volume provides an overview of a non asymptotic theory for model selection. It also discusses some selected applications to variable selection, change points detection and statistical learning.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Exponential and Information Inequalities
8 other sections not shown
Other editions - View all
absolute constant adaptive estimation assume assumption belongs Cauchy-Schwarz inequality centered choose collection of models compute concentration inequalities condition convex Corollary countable defined definition denotes density derive distribution ellipsoid empirical processes empirical risk Entp Euclidean exponential F Univ finite dimensional following inequality holds framework Gaussian measure Gaussian process given Hellinger Hellinger distance Hence implies independent random integer isonormal process Jensen's inequality Kullback-Leibler leads least squares Lemma linear linear span Lipschitz means measurable functions metric entropy minimax minimax lower bound minimax risk model selection model Sm Moreover nonincreasing nonnegative orthonormal basis p-body parameter partition pen(m penalized LSE penalty function piecewise positive constant positive number probability measure problem proof Proposition Rademacher random variables random vectors real number regression respect result risk bound satisfies set of probability space subset supremum supteT tensorization inequality type inequality upper bound