Logo - springer
Slogan - springer

Mathematics - Probability Theory and Stochastic Processes | Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery… - École d’Été de

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems

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

Koltchinskii, Vladimir

2011, IX, 254p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$39.95

(net) price for USA

ISBN 978-3-642-22147-7

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$59.95

(net) price for USA

ISBN 978-3-642-22146-0

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • 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
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.

Content Level » Research

Keywords » 62J99, 62H12, 60B20, 60G99 - concentration inequalities - empirical processes - low rank matrix recovery - sparse recovery

Related subjects » Probability Theory and Stochastic Processes

Table of contents / Preface / Sample pages 

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Probability Theory and Stochastic Processes.