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Improved Classification Rates for Localized Algorithms under Margin Conditions

  • Book
  • © 2020

Overview

Authors:
  1. Ingrid Karin Blaschzyk

    1. Stuttgart, Germany

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  • Study in the field of natural sciences

  • Study in the field of statistical learning theory

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction

    • Ingrid Karin Blaschzyk
    Pages 1-4

  3. Preliminaries

    • Ingrid Karin Blaschzyk
    Pages 5-34

  4. Histogram Rule: Oracle Inequality and Learning Rates

    • Ingrid Karin Blaschzyk
    Pages 35-57

  5. Localized SVMs: Oracle Inequalities and Learning Rates

    • Ingrid Karin Blaschzyk
    Pages 59-113

  6. Discussion

    • Ingrid Karin Blaschzyk
    Pages 115-116

  7. Back Matter

    Pages 117-126
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Keywords

About this book

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.

Authors and Affiliations

  • Stuttgart, Germany

    Ingrid Karin Blaschzyk

About the author

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

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