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 45
Sivu x
... Risk Minimization 49 4.6 5.1 Minimizing Other Criteria Problems and Exercises 5 Nearest Neighbor Rules Introduction 5555 54 56 5.2 Notation and Simple Asymptotics 5.3 Proof of Stone's Lemma 5.4 The Asymptotic Probability of Error 05888 ...
... Risk Minimization 49 4.6 5.1 Minimizing Other Criteria Problems and Exercises 5 Nearest Neighbor Rules Introduction 5555 54 56 5.2 Notation and Simple Asymptotics 5.3 Proof of Stone's Lemma 5.4 The Asymptotic Probability of Error 05888 ...
Sivu xii
... Risk Minimization 290 18.2 Poor Approximation Properties of VC Classes 18.3 Simple Empirical Covering 297 297 Problems and Exercises 300 19 Condensed and Edited Nearest Neighbor Rules 303 19.1 Condensed Nearest Neighbor Rules 303 19.2 ...
... Risk Minimization 290 18.2 Poor Approximation Properties of VC Classes 18.3 Simple Empirical Covering 297 297 Problems and Exercises 300 19 Condensed and Edited Nearest Neighbor Rules 303 19.1 Condensed Nearest Neighbor Rules 303 19.2 ...
Sivu 5
... risk min- imization , a method studied in great detail in the work of Vapnik and Chervonenkis ( 1971 ) . For example , if we select gn from C by minimizing n Σ Σ ( 82 ( Xi ) ¥¥ i ) • i = 1 n then the corresponding probability of error L ...
... risk min- imization , a method studied in great detail in the work of Vapnik and Chervonenkis ( 1971 ) . For example , if we select gn from C by minimizing n Σ Σ ( 82 ( Xi ) ¥¥ i ) • i = 1 n then the corresponding probability of error L ...
Sivu 6
... risk minimization produces a random data - dependent k that is not even guaranteed to tend to infinity or to be o ( m ) , yet the selected rule is universally consistent . = We offer virtually no help with algorithms as in standard ...
... risk minimization produces a random data - dependent k that is not even guaranteed to tend to infinity or to be o ( m ) , yet the selected rule is universally consistent . = We offer virtually no help with algorithms as in standard ...
Sivu 11
... risk . The proof given above reveals that L ( g ) = 1 − E { I { g ( x ) = 1 } N ( X ) + I { g ( x ) = 0 } ( 1 − n ... minimizing the absolute error E { | ƒ ( X ) — Y ] } is even more closely related to the Bayes rule ( see Problem 2.12 ) ...
... risk . The proof given above reveals that L ( g ) = 1 − E { I { g ( x ) = 1 } N ( X ) + I { g ( x ) = 0 } ( 1 − n ... minimizing the absolute error E { | ƒ ( X ) — Y ] } is even more closely related to the Bayes rule ( see Problem 2.12 ) ...
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