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 Mc Gill University (Montreal).
Tabella dei contenuti
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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