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Measures of Complexity

Festschrift for Alexey Chervonenkis

  • Book
  • © 2015

Overview

Editors:
  1. Vladimir Vovk

    1. Dept. of Computer Science, Royal Holloway, Univ of London, Egham, United Kingdom

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  2. Harris Papadopoulos

    1. Frederick University, Nicosia, Cyprus

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  3. Alexander Gammerman

    1. Dept. of Computer Science, University of London, Egham, United Kingdom

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  • Alexey Chervonenkis made an outstanding contribution to the areas of pattern recognition and computational learning
  • Valuable for researchers and graduate students
  • Contributors are leading scientists in statistics, theoretical computer science, and mathematics
  • Includes supplementary material: sn.pub/extras

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xxxi
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  3. Reviews of Measures of Complexity

    1. Front Matter

      Pages 55-56
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    2. VC Dimension, Fat-Shattering Dimension, Rademacher Averages, and Their Applications

      • Vladimir V. V’yugin
      Pages 57-74

    3. Around Kolmogorov Complexity: Basic Notions and Results

      • Alexander Shen
      Pages 75-115

    4. Predictive Complexity for Games with Finite Outcome Spaces

      • Yuri Kalnishkan
      Pages 117-139

  4. Making VC Bounds More Accurate

    1. Front Matter

      Pages 141-142
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    2. Making Vapnik–Chervonenkis Bounds Accurate

      • Léon Bottou
      Pages 143-155

    3. Comment: Transductive PAC-Bayes Bounds Seen as a Generalization of Vapnik–Chervonenkis Bounds

      • Olivier Catoni
      Pages 157-160

    4. Comment: The Two Styles of VC Bounds

      • Vladimir Vovk
      Pages 161-164

    5. Rejoinder: Making VC Bounds Accurate

      • Léon Bottou
      Pages 165-166

  5. Advances in VC Theory

    1. Front Matter

      Pages 167-169
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    2. Measures of Complexity in the Theory of Machine Learning

      • Alexey Chervonenkis
      Pages 171-183

    3. Classes of Functions Related to VC Properties

      • R. M. Dudley
      Pages 185-196

    4. On Martingale Extensions of Vapnik–Chervonenkis Theory with Applications to Online Learning

      • Alexander Rakhlin, Karthik Sridharan
      Pages 197-215
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Keywords

About this book

This book brings together historical notes, reviews of research developments, fresh ideas on how to make VC (Vapnik–Chervonenkis) guarantees tighter, and new technical contributions in the areas of machine learning, statistical inference, classification, algorithmic statistics, and pattern recognition.

The contributors are leading scientists in domains such as statistics, mathematics, and theoretical computer science, and the book will be of interest to researchers and graduate students in these domains.

Editors and Affiliations

  • Dept. of Computer Science, Royal Holloway, Univ of London, Egham, United Kingdom

    Vladimir Vovk

  • Frederick University, Nicosia, Cyprus

    Harris Papadopoulos

  • Dept. of Computer Science, University of London, Egham, United Kingdom

    Alexander Gammerman

Bibliographic Information

  • Book Title: Measures of Complexity

  • Book Subtitle: Festschrift for Alexey Chervonenkis

  • Editors: Vladimir Vovk, Harris Papadopoulos, Alexander Gammerman

  • DOI: https://doi.org/10.1007/978-3-319-21852-6

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-21851-9Published: 14 September 2015

  • Softcover ISBN: 978-3-319-35778-2Published: 22 October 2016

  • eBook ISBN: 978-3-319-21852-6Published: 03 September 2015

  • Edition Number: 1

  • Number of Pages: XXXI, 399

  • Number of Illustrations: 17 b/w illustrations, 30 illustrations in colour

  • Topics: Artificial Intelligence, Statistical Theory and Methods, Probability and Statistics in Computer Science, Optimization

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