A probabilistic theory of pattern recognition / Luc Devroye, László Györfi, Gábor Lugosi.

Includes bibliographical references (p. [593]-618) and indexes.

1. Introduction -- 2. The Bayes Error -- 3. Inequalities and Alternate Distance Measures -- 4. Linear Discrimination -- 5. Nearest Neighbor Rules -- 6. Consistency -- 7. Slow Rates of Convergence -- 8. Error Estimation -- 9. The Regular Histogram Rule -- 10. Kernel Rules -- 11. Consistency of the k-Nearest Neighbor Rule -- 12. Vapnik-Chervonenkis Theory -- 13. Combinatorial Aspects of Vapnik-Chervonenkis Theory -- 14. Lower Bounds for Empirical Classifier Selection -- 15. The Maximum Likelihood Principle -- 16. Parametric Classification -- 17. Generalized Linear Discrimination -- 18. Complexity Regularization -- 19. Condensed and Edited Nearest Neighbor Rules -- 20. Tree Classifiers -- 21. Data-Dependent Partitioning -- 22. Splitting the Data -- 23. The Resubstitution Estimate -- 24. Deleted Estimates of the Error Probability -- 25. Automatic Kernel Rules -- 26. Automatic Nearest Neighbor Rules -- 27. Hypercubes and Discrete Spaces --

28. Epsilon Entropy and Totally Bounded Sets -- 29. Uniform Laws of Large Numbers -- 30. Neural Networks -- 31. Other Error Estimates -- 32. Feature Extraction.

Pattern recognition presents one of the most significant challenges for scientists and engineers, and many different approaches have been proposed. The aim of this book is to provide a self-contained account of probabilistic analysis of these approaches. The book includes a discussion of distance measures, nonparametric methods based on kernels or nearest neighbors, Vapnik-Chervonenkis theory, epsilon entropy, parametric classification, error estimation, tree classifiers, and neural networks.

Wherever possible, distribution-free properties and inequalities are derived. A substantial portion of the results or the analysis is new. Over 430 problems and exercises complement the material.