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Introduction

  • Vladimir KoltchinskiiEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2033)

Abstract

We start with a brief overview of empirical risk minimization problems and of the role of empirical and Rademacher processes in constructing distribution dependent and data dependent excess risk bounds. We then discuss penalized empirical risk minimization and oracle inequalities and conclude with sparse recovery and low rank matrix recovery problems. Many important aspects of empirical risk minimization are beyond the scope of these notes, in particular, the circle of questions related to approximation theory (see well known papers by Cucker and Smale [47], DeVore et al. [49] and references therein).

Keywords

Excess Risk Empirical Process Reproduce Kernel Hilbert Space Matrix Completion Hinge Loss 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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