Lectures on the Nearest Neighbor Method
Springer International Publishing (Verlag)
978-3-319-25386-2 (ISBN)
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).
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.
"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)
| Erscheinungsdatum | 08.10.2016 |
|---|---|
| Reihe/Serie | Springer Series in the Data Sciences |
| Zusatzinfo | IX, 290 p. 4 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 604 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | Density Estimation • mathematics and statistics • Nearest Neighbor Method • order statistics • pattern recognition • Probability theory and stochastic processes • regression estimation • Statistics and Computing/Statistics Programs • Stone's theorem |
| ISBN-10 | 3-319-25386-7 / 3319253867 |
| ISBN-13 | 978-3-319-25386-2 / 9783319253862 |
| Zustand | Neuware |
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