A Probabilistic Theory of Pattern RecognitionSpringer Science & Business Media, 27.11.2013 - 638 sivua 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. |
Kirjan sisältä
Tulokset 1 - 5 kokonaismäärästä 58
Sivu x
... Rules When L * = 0 80 81 81 83 91 91 6.2 Classification and Regression Estimation 92 6.3 Partitioning Rules 94 6.4 The Histogram Rule 95 6.5 Stone's Theorem 97 6.6 The k - Nearest Neighbor Rule 100 6.7 Classification Is Easier Than ...
... Rules When L * = 0 80 81 81 83 91 91 6.2 Classification and Regression Estimation 92 6.3 Partitioning Rules 94 6.4 The Histogram Rule 95 6.5 Stone's Theorem 97 6.6 The k - Nearest Neighbor Rule 100 6.7 Classification Is Easier Than ...
Sivu xi
... Histogram Rule 133 9.1 The Method of Bounded Differences 133 9.2 Strong Universal Consistency 138 Problems and Exercises 10 Kernel Rules 142 147 10.1 Consistency 10.2 Proof of the Consistency Theorem 10.3 Potential Function Rules ...
... Histogram Rule 133 9.1 The Method of Bounded Differences 133 9.2 Strong Universal Consistency 138 Problems and Exercises 10 Kernel Rules 142 147 10.1 Consistency 10.2 Proof of the Consistency Theorem 10.3 Potential Function Rules ...
Sivu xiii
... Histograms and Rule Selection Problems and Exercises 403 405 24 Deleted Estimates of the Error Probability 407 24.1 A General Lower Bound 408 24.2 A General Upper Bound for Deleted Estimates 24.3 Nearest Neighbor Rules 411 413 24.5 ...
... Histograms and Rule Selection Problems and Exercises 403 405 24 Deleted Estimates of the Error Probability 407 24.1 A General Lower Bound 408 24.2 A General Upper Bound for Deleted Estimates 24.3 Nearest Neighbor Rules 411 413 24.5 ...
Sivu 8
... rules 6 Consistency 7 Slow rates of convergence 8 Error estimation ( 32 ) 15 9 The regular histogram rule 10 Kernel rules 12 Vapnik - Chervonenkis theory 11 Consistency of the k - nearest neighbor rule 27 13 Combinatorial aspects of ...
... rules 6 Consistency 7 Slow rates of convergence 8 Error estimation ( 32 ) 15 9 The regular histogram rule 10 Kernel rules 12 Vapnik - Chervonenkis theory 11 Consistency of the k - nearest neighbor rule 27 13 Combinatorial aspects of ...
Sivu 95
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Sisältö
1 | |
4 | |
21 | |
27 | |
54 | |
Nearest Neighbor Rules | 60 |
4 | 67 |
6 | 74 |
Parametric Classification | 263 |
Generalized Linear Discrimination | 279 |
Complexity Regularization | 289 |
Condensed and Edited Nearest Neighbor Rules 303 | 302 |
Tree Classifiers | 315 |
DataDependent Partitioning | 363 |
Splitting the Data 387 | 386 |
The Resubstitution Estimate | 397 |
11 | 81 |
2 | 92 |
6 | 100 |
8 | 106 |
2 | 113 |
Error Estimation | 120 |
The Regular Histogram Rule | 133 |
Kernel Rules | 153 |
Consistency of the kNearest Neighbor Rule | 168 |
VapnikChervonenkis Theory | 187 |
Combinatorial Aspects of VapnikChervonenkis Theory | 214 |
4 | 224 |
1 | 234 |
The Maximum Likelihood Principle | 249 |
Deleted Estimates of the Error Probability | 407 |
Automatic Kernel Rules 423 | 422 |
Automatic Nearest Neighbor Rules | 451 |
Hypercubes and Discrete Spaces 461 | 460 |
Epsilon Entropy and Totally Bounded Sets | 479 |
Uniform Laws of Large Numbers 489 | 488 |
Neural Networks | 507 |
Other Error Estimates | 549 |
Feature Extraction 561 | 560 |
Appendix | 575 |
Notation | 591 |
Author Index | 619 |
Subject Index | 627 |
Muita painoksia - Näytä kaikki
A Probabilistic Theory of Pattern Recognition Luc Devroye,László Györfi,Gabor Lugosi Rajoitettu esikatselu - 1997 |
A Probabilistic Theory of Pattern Recognition Luc Devroye,Laszlo Gyorfi,Gábor Lugosi Esikatselu ei käytettävissä - 2014 |
A Probabilistic Theory of Pattern Recognition Luc Devroye,László Györfi,Gabor Lugosi Esikatselu ei käytettävissä - 2013 |
Yleiset termit ja lausekkeet
a₁ algorithm Assume asymptotic b₁ Bayes error binary Cauchy-Schwarz inequality cells Chapter class of classifiers classification rule condition converges to zero Corollary data points decision defined deleted estimate denotes density Devroye distribution empirical error error estimate error probability example finite fixed function HINT histogram rule Hoeffding's inequality hyperplane hyperrectangles inequality integer Jensen's inequality k-d tree k-nearest k-NN rule kernel rule L(gn Lemma linear classifier maximum likelihood minimizing the empirical nearest neighbor rule neural network node obtained otherwise pairs parameters partition pattern recognition probability of error proof of Theorem Prove random variables rate of convergence rectangles risk minimization rule gn sample selected shatter coefficients Show sigmoid split squared error structural risk minimization subsets tree classifiers universally consistent upper bound values vc dimension vector X₁ Y₁ фес