Lectures on the Nearest Neighbor Method

AvGérard Biau,Luc Devroye

Inbunden, Engelska, 2015

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Beskrivning

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).

Produktinformation

Utgivningsdatum:2015-12-15
Mått:155 x 235 x 22 mm
Vikt:617 g
Format:Inbunden
Språk:Engelska
Serie:Springer Series in the Data Sciences
Antal sidor:290
Upplaga:15001
Förlag:Springer International Publishing AG
ISBN:9783319253862

Utforska kategorier

Systemvetenskap och AI inom Data och IT
Matematisk statistik inom Naturvetenskap och teknik
Affärsapplikationer inom Data och IT

Recensioner i media

"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)

Innehållsförteckning

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.