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Improved Classification Rates for Localized Algorithms under Margin Conditions

  • Ingrid Karin Blaschzyk
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Table of contents

  1. Front Matter
    Pages I-XV
  2. Ingrid Karin Blaschzyk
    Pages 1-4
  3. Ingrid Karin Blaschzyk
    Pages 5-34
  4. Ingrid Karin Blaschzyk
    Pages 35-57
  5. Ingrid Karin Blaschzyk
    Pages 59-113
  6. Ingrid Karin Blaschzyk
    Pages 115-116
  7. Back Matter
    Pages 117-126

About this book

Introduction

Support vector machines (SVMs) are one of the most successful algorithms on small and medium-sized data sets, but on large-scale data sets their training and predictions become computationally infeasible. The author considers a spatially defined data chunking method for large-scale learning problems, leading to so-called localized SVMs, and implements an in-depth mathematical analysis with theoretical guarantees, which in particular include classification rates. The statistical analysis relies on a new and simple partitioning based technique and takes well-known margin conditions into account that describe the behavior of the data-generating distribution. It turns out that the rates outperform known rates of several other learning algorithms under suitable sets of assumptions. From a practical point of view, the author shows that a common training and validation procedure achieves the theoretical rates adaptively, that is, without knowing the margin parameters in advance.

Contents

  • Introduction to Statistical Learning Theory
  • Histogram Rule: Oracle Inequality and Learning Rates
  • Localized SVMs: Oracle Inequalities and Learning Rates

Target Groups

Researchers, students, and practitioners in the fields of mathematics and computer sciences who focus on machine learning or statistical learning theory

The Author

Ingrid Karin Blaschzyk is a postdoctoral researcher in the Department of Mathematics at the University of Stuttgart, Germany.

Keywords

Classification Learning Rates Gaussian Kernel Tsybakov Noise Localized SVMs Support Vector Machines (SVMs) Hinge Loss Spatial Decomposition Histogram Rule Oracle Inequality

Authors and affiliations

  • Ingrid Karin Blaschzyk
    • 1
  1. 1.StuttgartGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-658-29591-2
  • Copyright Information Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2020
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-658-29590-5
  • Online ISBN 978-3-658-29591-2
  • Buy this book on publisher's site