Improved Classification Rates for Localized Algorithms under Margin Conditions

1. Auflage 2020
ISBN: 978-3-658-29590-5
Verlag: Springer

Buch, Englisch, 126 Seiten, Format (B × H): 148 mm x 210 mm, Gewicht: 197 g

Reihe: Research

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.

Zielgruppe

Research

Autoren/Hrsg.

Blaschzyk, Ingrid Karin

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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

Über Autor(innen)

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