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Improved Classification Rates for Localized Algorithms under Margin Conditions - Softcover

Blaschzyk, Ingrid Karin

 
9783658295905: Improved Classification Rates for Localized Algorithms under Margin Conditions
Softcover
ISBN 10: 3658295902 ISBN 13: 9783658295905
Publisher: Springer Spektrum, 2020

Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

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

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer Spektrum
Publication date
2020
Language
English
ISBN 10 
3658295902
ISBN 13 
9783658295905
Binding
Paperback
Edition number
1
Number of pages
141