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  • © 2015

Lectures on the Nearest Neighbor Method

  • Presents a rigorous overview of nearest neighbor methods
  • Many different components covered: statistical, probabilistic, combinatorial, and geometric ideas
  • Extensive appendix material provided

Part of the book series: Springer Series in the Data Sciences (SSDS)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-ix
  2. Density estimation

    1. Front Matter

      Pages 1-1
    2. Order statistics and nearest neighbors

      • Gérard Biau, Luc Devroye
      Pages 3-11
    3. The nearest neighbor distance

      • Gérard Biau, Luc Devroye
      Pages 13-23
    4. The k-nearest neighbor density estimate

      • Gérard Biau, Luc Devroye
      Pages 25-32
    5. Uniform consistency

      • Gérard Biau, Luc Devroye
      Pages 33-42
    6. Weighted k-nearest neighbor density estimates

      • Gérard Biau, Luc Devroye
      Pages 43-51
    7. Local behavior

      • Gérard Biau, Luc Devroye
      Pages 53-73
    8. Entropy estimation

      • Gérard Biau, Luc Devroye
      Pages 75-91
  3. Regression estimation

    1. Front Matter

      Pages 93-93
    2. The nearest neighbor regression function estimate

      • Gérard Biau, Luc Devroye
      Pages 95-103
    3. The 1-nearest neighbor regression function estimate

      • Gérard Biau, Luc Devroye
      Pages 105-110
    4. L p-consistency and Stone’s theorem

      • Gérard Biau, Luc Devroye
      Pages 111-130
    5. Pointwise consistency

      • Gérard Biau, Luc Devroye
      Pages 131-151
    6. Uniform consistency

      • Gérard Biau, Luc Devroye
      Pages 153-164
    7. Advanced properties of uniform order statistics

      • Gérard Biau, Luc Devroye
      Pages 165-173
    8. Rates of convergence

      • Gérard Biau, Luc Devroye
      Pages 175-192
    9. Regression: the noiseless case

      • Gérard Biau, Luc Devroye
      Pages 193-210
    10. The choice of a nearest neighbor estimate

      • Gérard Biau, Luc Devroye
      Pages 211-220
  4. Supervised classification

    1. Front Matter

      Pages 221-221

About this book

This text presents a wide-ranging and rigorous overview of nearest neighbor methods, one of the most important paradigms in machine learning. Now in one self-contained volume, this book systematically covers key statistical, probabilistic, combinatorial and geometric ideas for understanding, analyzing and developing nearest neighbor methods.

Gérard Biau is a professor at Université Pierre et Marie Curie (Paris). Luc Devroye is a professor at the School of Computer Science at McGill University (Montreal).   

Reviews

“This book deals with different aspects regarding this approach, starting with the standard k-nearest neighbor model, and passing through the weighted k-nearest neighbor model, estimations for entropy, regression functions etc. … It is intended for a large audience, including students, teachers, and researchers.” (Florin Gorunescu, zbMATH 1330.68001, 2016)

   

Authors and Affiliations

  • Universite Pierre et Marie Curie, Paris Cedex 05, France

    Gérard Biau

  • School of Computer Science, McGill University, Montreal, Canada

    Luc Devroye

Bibliographic Information

Buy it now

Buying options

eBook USD 59.99 USD 119.00
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99 USD 159.99
50% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 79.99 USD 159.99
50% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access