École d'Été de Probabilités de Saint-Flour

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems

École d’Été de Probabilités de Saint-Flour XXXVIII-2008

Authors: Koltchinskii, Vladimir

  • Provides a unified framework for machine learning problems (such as large margin
  • classification), sparse recovery and low rank matrix problems
  • Develops a variety of probabilistic inequalities for empirical processes needed to obtain error bounds
  • in machine learning and sparse recovery
  • Develops a comprehensive theory of excess risk bounds and oracle inequalities for penalized empirical
  • risk minimization
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About this book

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 in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.

Reviews

From the reviews:

“The book is an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. … The book is interesting and useful for students as well as for professionals in the field of probability theory, statistics, and their applications.” (Pavel Stoynov, Zentralblatt MATH, Vol. 1223, 2011)


Table of contents (9 chapters)

  • Introduction

    Koltchinskii, Vladimir

    Pages 1-16

  • Empirical and Rademacher Processes

    Koltchinskii, Vladimir

    Pages 17-32

  • Bounding Expected Sup-Norms of Empirical and Rademacher Processes

    Koltchinskii, Vladimir

    Pages 33-57

  • Excess Risk Bounds

    Koltchinskii, Vladimir

    Pages 59-79

  • Examples of Excess Risk Bounds in Prediction Problems

    Koltchinskii, Vladimir

    Pages 81-97

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-22147-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-22146-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems
Book Subtitle
École d’Été de Probabilités de Saint-Flour XXXVIII-2008
Authors
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
2033
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-22147-7
DOI
10.1007/978-3-642-22147-7
Softcover ISBN
978-3-642-22146-0
Series ISSN
0721-5363
Edition Number
1
Number of Pages
IX, 254
Topics