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Lectures on the Nearest Neighbor Method / by Gérard Biau, Luc Devroye.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Author/Creator:
- Biau, Gérard., Author.
- Devroye, Luc., Author.
- Series:
- Springer Series in the Data Sciences, 2365-5674
- Language:
- English
- Subjects (All):
- Probabilities.
- Pattern perception.
- Statistics.
- Probability Theory and Stochastic Processes.
- Pattern Recognition.
- Statistics and Computing/Statistics Programs.
- Local Subjects:
- Probability Theory and Stochastic Processes.
- Pattern Recognition.
- Statistics and Computing/Statistics Programs.
- Physical Description:
- IX, 290 p. ; : il. en col.
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2015.
- Summary:
- 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). .
- Contents:
- 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
- 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.
- Notes:
- MSC 68Wxx ; 60Exx ; 62Exx ; 68T10
- Includes bibliographical references and index.
- ISBN:
- 3-319-25388-3
- Online:
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