Lectures on the Nearest Neighbor Method

by Gérard Biau, Luc Devroye

Overview

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).   

Product Details

ISBN-13:	9783319797823
Publisher:	Springer International Publishing
Publication date:	03/20/2019
Series:	Springer Series in the Data Sciences
Edition description:	Softcover reprint of the original 1st ed. 2015
Pages:	290
Product dimensions:	6.10(w) x 9.25(h) x (d)

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.

Editorial 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)

From the Publisher