A Probabilistic Theory of Pattern Recognition

by Devroye, Luc; Gyorfi, Laszlo; Lugosi, Gabor

• ISBN13: 9780387946184
• ISBN10: 0387946187
• Format: Hardcover
• Copyright: 1996-01-01
• Publisher: Springer Verlag

Summary

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, free 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.

Table of Contents

Preface
Introduction	p. 1
The Bayes Error	p. 9
Inequalities and Alternate Distance Measures	p. 21
Linear Discrimination	p. 39
Nearest Neighbor Rules	p. 61
Consistency	p. 91
Slow Rates of Convergence	p. 111
Error Estimation	p. 121
The Regular Histogram Rule	p. 133
Kernel Rules	p. 147
Consistency of the k-Nearest Neighbor Rule	p. 169
Vapnik-Chervonenkis Theory	p. 187
Combinatorial Aspects of Vapnik-Chervonenkis Theory	p. 215
Lower Bounds for Empirical Classifier Selection	p. 233
The Maximum Likelihood Principle	p. 249
Parametric Classification	p. 263
Generalized Linear Discrimination	p. 279
Complexity Regularization	p. 289
Condensed and Edited Nearest Neighbor Rules	p. 303
Tree Classifiers	p. 315
Data-Dependent Partitioning	p. 363
Splitting the Data	p. 387
The Resubstitution Estimate	p. 397
Deleted Estimates of the Error Probability	p. 407
Automatic Kernel Rules	p. 423
Automatic Nearest Neighbor Rules	p. 451
Hypercubes and Discrete Spaces	p. 461
Epsilon Entropy and Totally Bounded Sets	p. 479
Uniform Laws of Large Numbers	p. 489
Neural Networks	p. 507
Other Error Estimates	p. 549
Feature Extraction	p. 561
Appendix	p. 575
Notation	p. 591
References	p. 593
Author Index	p. 619
Subject Index	p. 627
Table of Contents provided by Blackwell. All Rights Reserved.