Lectures on the Nearest Neighbor Method

Lectures on the Nearest Neighbor Method

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, analyzi...

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Bibliographic Details
Published in:Springer eBooks
Main Authors: Biau, Gérard (Author), Devroye, Luc (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Series:Springer Series in the Data Sciences,
Subjects:
mathematics.
Pattern Recognition.
Probabilities.
Statistics.
Mathematics.
Probability Theory and Stochastic Processes.
Statistics and Computing/Statistics Programs.
Online Access:http://dx.doi.org/10.1007/978-3-319-25388-6
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Table of Contents:
  • Part I: Density Estimation
  • Order Statistics and Nearest Neighbors
  • The Expected Nearest Neighbor Distance
  • The k-nearest Neighbor Density Estimate
  • Uniform Consistency
  • Weighted k-nearest neighbor density estimates.- Local Behavior
  • Entropy Estimation
  • Part II: Regression Estimation
  • The Nearest Neighbor Regression Function Estimate
  • The 1-nearest Neighbor Regression Function Estimate
  • LP-consistency and Stone's Theorem
  • Pointwise Consistency
  • Uniform Consistency
  • Advanced Properties of Uniform Order Statistics
  • Rates of Convergence
  • Regression: The Noisless Case
  • The Choice of a Nearest Neighbor Estimate
  • Part III: Supervised Classification
  • Basics of Classification
  • The 1-nearest Neighbor Classification Rule
  • The Nearest Neighbor Classification Rule. Appendix
  • Index.

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