Lectures on the Nearest Neighbor Method electronic resource by Gérard Biau, Luc Devroye.
Material type: TextSeries: Springer Series in the Data SciencesPublication details: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 1st ed. 2015Description: IX, 290 p. 4 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319253886Subject(s): mathematics | Pattern Recognition | Probabilities | Statistics | Mathematics | Probability Theory and Stochastic Processes | Pattern Recognition | Statistics and Computing/Statistics ProgramsDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access onlinePart 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 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). .
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