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 81
Sivu 2
... fixed . Averaging over the data as well would be unnatural , because in a given application , one has to live with the data at hand . It would be marginally useful to know the number EL , as this number would indicate the quality of an ...
... fixed . Averaging over the data as well would be unnatural , because in a given application , one has to live with the data at hand . It would be marginally useful to know the number EL , as this number would indicate the quality of an ...
Sivu 28
... fixed L * , any value of J above the lower bound is possible for some distribution of ( X , Y ) . From the definition of J , we see that J = 0 if and only if n = 1/2 with probability one , or L * = 1/2 . 1 AJ FIGURE 3.4 . This figure ...
... fixed L * , any value of J above the lower bound is possible for some distribution of ( X , Y ) . From the definition of J , we see that J = 0 if and only if n = 1/2 with probability one , or L * = 1/2 . 1 AJ FIGURE 3.4 . This figure ...
Sivu 32
... fixed class probabilities , an F - error is small if the two conditional distributions are " far away " from each other . A metric quantifying this distance may be defined as follows . Let f : [ 0 , ∞ ) → → RU { −∞ , ∞ } be a ...
... fixed class probabilities , an F - error is small if the two conditional distributions are " far away " from each other . A metric quantifying this distance may be defined as follows . Let f : [ 0 , ∞ ) → → RU { −∞ , ∞ } be a ...
Sivu 35
... fixed Rd - valued random variable , and define î1 ( x ) = P { Y1 = 1 | X = x } , n2 ( x ) = P { Y2 = 1 | X = x } , where Y1 , Y2 are Bernoulli random variables . Clearly , n ( x ) = pn1 ( x ) + ( 1 − p ) n2 ( x ) . Which of the error ...
... fixed Rd - valued random variable , and define î1 ( x ) = P { Y1 = 1 | X = x } , n2 ( x ) = P { Y2 = 1 | X = x } , where Y1 , Y2 are Bernoulli random variables . Clearly , n ( x ) = pn1 ( x ) + ( 1 − p ) n2 ( x ) . Which of the error ...
Sivu 50
... fixed manner . Next we show that the classifier corresponding to is really very good . FIGURE 4.5 . If the data points are in general position , then for each linear rule there exists a linear split defined by a hyperplane crossing d ...
... fixed manner . Next we show that the classifier corresponding to is really very good . FIGURE 4.5 . If the data points are in general position , then for each linear rule there exists a linear split defined by a hyperplane crossing d ...
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