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 83
Sivu x
... Probability of Error 05888 61 61 63 66 69 5.5 The Asymptotic Error Probability of Weighted Nearest Neighbor Rules 71 5.6 k - Nearest Neighbor Rules : Even k 74 5.7 Inequalities for the Probability of Error 75 5.8 5.9 6.1 Behavior When L ...
... Probability of Error 05888 61 61 63 66 69 5.5 The Asymptotic Error Probability of Weighted Nearest Neighbor Rules 71 5.6 k - Nearest Neighbor Rules : Even k 74 5.7 Inequalities for the Probability of Error 75 5.8 5.9 6.1 Behavior When L ...
Sivu 2
Luc Devroye, Laszlo Györfi, Gabor Lugosi. random pair . The distribution of ( X , Y ) describes the frequency of encountering particular pairs in practice . An error occurs if g ( X ) 7 Y , and the probability of error for a classifier g ...
Luc Devroye, Laszlo Györfi, Gabor Lugosi. random pair . The distribution of ( X , Y ) describes the frequency of encountering particular pairs in practice . An error occurs if g ( X ) 7 Y , and the probability of error for a classifier g ...
Sivu 5
... probability of error is better than for any k - nearest neighbor classifier with k > 1. So , it can never be totally dismissed . Thus , we must study all simple rules , and we will reserve many pages for the nearest neighbor rule and ...
... probability of error is better than for any k - nearest neighbor classifier with k > 1. So , it can never be totally dismissed . Thus , we must study all simple rules , and we will reserve many pages for the nearest neighbor rule and ...
Sivu 10
... distribution of ( X , Y ) is deter- mined by ( μ , n ) . The function ʼn is sometimes called the a posteriori probability . η Any function g : Rd → { 0 , 1 } defines a classifier or a decision function . The error probability of g is L ...
... distribution of ( X , Y ) is deter- mined by ( μ , n ) . The function ʼn is sometimes called the a posteriori probability . η Any function g : Rd → { 0 , 1 } defines a classifier or a decision function . The error probability of g is L ...
Sivu 11
... probability of error , Bayes error , or Bayes risk . The proof given above reveals that L ( g ) = 1 − E { I { g ( x ) = 1 } N ( X ) + I { g ( x ) = 0 } ( 1 − n ( X ) ) } , and in particular , L * = 1 − E { I { n ( x ) > 1/2 } N ( X ) ...
... probability of error , Bayes error , or Bayes risk . The proof given above reveals that L ( g ) = 1 − E { I { g ( x ) = 1 } N ( X ) + I { g ( x ) = 0 } ( 1 − n ( X ) ) } , and in particular , L * = 1 − E { I { n ( x ) > 1/2 } N ( X ) ...
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