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 84
Sivu 7
... denotes a Borel set , and so forth . If we need many kinds of sets , we will typically use the beginning of the ... denote classes of functions or sets . A short list of frequently used symbols is found at the end of the book . At the ...
... denotes a Borel set , and so forth . If we need many kinds of sets , we will typically use the beginning of the ... denote classes of functions or sets . A short list of frequently used symbols is found at the end of the book . At the ...
Sivu 10
... denotes the indicator of the set A. Thus , for every x € Rd , P { g ( X ) YX = x } − P { g * ( X ) Y \ X = x } = = · ― - n ( x ) ( I { g * ( x ) = 1 } — I { g ( x ) = 1 } ) + ( 1 − n ( x ) ) ( I { g * ( x ) = 0 } — I ( g ( x ) = 0 ) ...
... denotes the indicator of the set A. Thus , for every x € Rd , P { g ( X ) YX = x } − P { g * ( X ) Y \ X = x } = = · ― - n ( x ) ( I { g * ( x ) = 1 } — I { g ( x ) = 1 } ) + ( 1 − n ( x ) ) ( I { g * ( x ) = 0 } — I ( g ( x ) = 0 ) ...
Sivu 15
... denotes the positive part of a function g . Thus , the Bayes error is directly related to the L1 distance between the class densities . FIGURE 2.3 . The shaded area is the L1 distance between the class - conditional densities . The best ...
... denotes the positive part of a function g . Thus , the Bayes error is directly related to the L1 distance between the class densities . FIGURE 2.3 . The shaded area is the L1 distance between the class - conditional densities . The best ...
Sivu 19
... denote whether a student passes ( fails ) a course . Assume that Y = 1 if and only if TBE ≤ 8 . = ( 1 ) Find the Bayes decision if no variable is available , if only T is available , and if only T and B are available . ( 2 ) Determine ...
... denote whether a student passes ( fails ) a course . Assume that Y = 1 if and only if TBE ≤ 8 . = ( 1 ) Find the Bayes decision if no variable is available , if only T is available , and if only T and B are available . ( 2 ) Determine ...
Sivu 20
... denotes the positive part of a function f . The key observation is that convergence to zero of each term of the infinite sum implies convergence of the whole integral by the dominated convergence theorem , since ƒ ( fn ( x ) − f ( x ) ...
... denotes the positive part of a function f . The key observation is that convergence to zero of each term of the infinite sum implies convergence of the whole integral by the dominated convergence theorem , since ƒ ( fn ( x ) − f ( 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