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Lectures on the Nearest Neighbor Method
ISBN-13:
9783319253886
Veröffentl:
2015
Seiten:
290
Autor:
Gérard Biau
Serie:
Springer Series in the Data Sciences
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
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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