Improved Classification Rates for Localized Algorithms under Margin Conditions. 1st ed. 2020

種類:

電子ブック

責任表示:

by Ingrid Karin Blaschzyk

出版情報:

Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum, 2020

著者名:

• Blaschzyk, Ingrid Karin.
• SpringerLink (Online service)

ISBN:

9783658295912 [3658295910]    

注記:

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

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