Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems
The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments i
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further volumes: http://www.springer.com/series/304
2033
Saint-Flour Probability Summer School
The Saint-Flour volumes are reflections of the courses given at the Saint-Flour Probability Summer School. Founded in 1971, this school is organised every year by the Laboratoire de Math´ematiques (CNRS and Universit´e Blaise Pascal, Clermont-Ferrand, France). It is intended for PhD students, teachers and researchers who are interested in probability theory, statistics, and in their applications. The duration of each school is 13 days (it was 17 days up to 2005), and up to 70 participants can attend it. The aim is to provide, in three highlevel courses, a comprehensive study of some fields in probability theory or Statistics. The lecturers are chosen by an international scientific board. The participants themselves also have the opportunity to give short lectures about their research work. Participants are lodged and work in the same building, a former seminary built in the 18th century in the city of Saint-Flour, at an altitude of 900 m. The pleasant surroundings facilitate scientific discussion and exchange. The Saint-Flour Probability Summer School is supported by: – Universit´e Blaise Pascal – Centre National de la Recherche Scientifique (C.N.R.S.) – Minist`ere d´el´egu´e a` l’Enseignement sup´erieur et a` la Recherche For more information, see back pages of the book and http://math.univ-bpclermont.fr/stflour/ Jean Picard Summer School Chairman Laboratoire de Math´ematiques Universit´e Blaise Pascal 63177 Aubi`ere Cedex France
Vladimir Koltchinskii
Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems ´ ´ e de Probabilit´es Ecole d’Et´ de Saint-Flour XXXVIII-2008
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Prof. Vladimir Koltchinskii Georgia Institute of Technology School of Mathematics Atlanta USA [email protected]
ISBN 978-3-642-22146-0 e-ISBN 978-3-642-22147-7 DOI 10.1007/978-3-642-22147-7 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2011934366 Mathematics Subject Classification (2010): 62J99, 62H12, 60B20, 60G99 c Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general us
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