Vapnik V.N. — The nature of statistical learning theory :: Электронная библиотека попечительского совета мехмата МГУ

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Vapnik V.N. — The nature of statistical learning theory

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Название: The nature of statistical learning theory

Автор: Vapnik V.N.

Аннотация:

Discusses the fundamental ideas that lie behind the statistical theory of learning and generalization. Considers learning as a general problem of function estimation based on empirical data.

Язык:

Рубрика: Computer science/AI, knowledge/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2000

Количество страниц: 314

Добавлена в каталог: 23.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

approximation of the logistic regression      155
$\Delta$ -margin separating hyperplane      132
$\sigma$ -algebra      60
$\varepsilon$ -intensitive loss function      181
$\varepsilon$ -intensitivity      181
A posteriori information      120
a priori information      120
AdaBoost algorithm      163
Admissible structure      95
algorithmic complexity      10
Annealed entropy      55
ANOVA decomposition      199
Approximately defined operator      230
Approximation rate      98
artificial intelligence      13
Axioms of probability theory      60
Back propagation method      126
Basic problem of probability theory      62
Basic problem of statistics      63
Bayesian approach      119
Bayesian inference      34
Bound on the distance to the smallest risk      77
Bound on the value of achieved risk      77
Bounds on generalization ability of a learning machine      76
Canonical separating hyperplanes      132
Capacity control problem      116
Cause-effect relation      9
Choosing the best sparse algebraic polynomial      117
Choosing the degree of a polynomial      116
Classification error      19
Codebook      106
Complete (Popper's) nonfalsifiability      52
Compression coefficient      107
Conditional density estimation      228
Conditional probability estimation      227
Consistency of inference      36
Constructive distribution-independent bound on the rate of convergence      69
Convolution of inner product      140
Criterion of nonfalsifiability      47
Data smoothing problem      209
Decision trees      7
Decisionmaking problem      296
Deductive inference      47
Density estimation problem: nonparametric setting      28
Density estimation problem: parametric (Fisher — Wald) setting      19
Discrepancy      18
Discriminant analysis      24
Discriminant function      25
Distribution-dependent bound on the rate of convergence      69
Distribution-independent bound on the rate of convergence      69
Empirical distribution function      28
Empirical processes      40
Empirical risk functional      20
Empirical risk minimization inductive principle      20
Ensemble of support vector machines      163
Entropy of the set of functions      42
Entropy on the set of indicator functions      42
Equivalence classes      292
Estimation of the values of a function at the given points      292
Expert Systems      7
Feature selection problem      119
Function approximation      98
Function estimation model      17
Gaussian      279
Generalized Glivenko — Cantelli problem      66
Generalized growth function      85
Generator of random vectors      17
Glivenko — Cantelli problem      66
Growth function      55
Hamming distance      106
Handwritten digit recognition      147
Hard vicinity function      269
Hard-threshold vicinity function      103
Hidden Markov models      7
Hidden units      101
Huber loss function      183
ill-posed problems      9
Ill-posed problems: solution by quasi-solution method      236
Ill-posed problems: solution by residual method      236
Ill-posed problems: solution by variation method      236
Independent trials      62
Inductive inference      55
Inner product in Hilbert space      140
Integral equations: solution for approximately determined equations      239
Integral equations: solution for exact determined equations      238
Kernel function      27
Kolmogorov — Smirnov distribution      87
Kuhn — Tucker conditions      134
Kulback — Lcibler distance      32
Lagrange multiplier      134
Lagrangian      134
Laplacian      277
Law of Large Numbers      41
Law of large numbers in functional space      41
Law of large numbers in vector space      41
Learning machine      17
Learning matrices      7
Least-modulo method      182
Least-squares method      21
Lie derivatives      279
Linear discriminant function      31
Linearly nonseparable case      135
Local approximation      104
Local risk minimization      103

Locality parameter      103
Loss function: for AdaBoost algorithm      163
Loss function: for density estimation      21
Loss function: for logistic regression      156
Loss function: for patter recognition      21
Loss function: for regression estimation      21
MADALINE      7
Main principle for small sample size problems      31
Maximal margin hyperplane      131
Maximum likelihood method      24
McCulloch — Pitts neuron model      2
Measurements with the additive noise      25
Metric $\varepsilon$ -entropy      44
Minimum description length principle      104
Mixture of normal densities      26
National Institute of Standard and Technology (NIST) digit database      173
Neural networks      126
Nonparametric density estimation      27
Nontrivially consistent inference      38
Normal discriminant function      31
One-sided empirical process      40
Optimal separating hyperplane      131
Overfitting phenomenon      14
Parametric methods of density estimation      24
Partial nonfalsifiability      50
Parzen's windows method      27
Pattern recognition problem      19
Perceptron      1
Perceptron's stopping rule      6
Polynomial approximation of regression      116
Polynomial machine      143
Potential nonfalsifiability      53
Probability measure      59
Probably approximately correct (PAC) model      13
Problem of demarcation      49
Pseudo-dimension      90
Quadratic programming problem      133
Quantization of parameters      110
Quosi-solution      112
Radial basis function machine      145
Random entropy      42
Random string      10
Randomness concept      10
Regression estimation problem      19
Regression function      19
Regularization theory      9
Regularized functional      9
Reproducing kernel Hilbert space      244
Residual principle      236
Rigorous (distribution-dependent) bounds      85
Risk functional      18
Risk minimization from empirical data problem      20
Robust estimators      26
Robust regression      26
Rosenblatt's algorithm      5
Set of indicators      73
Set of unbounded functions      77
Sigmoid function      125
Small sample size      93
Smoothing kernel      102
Smoothness of functions      100
Soft threshold vicinity function      103
Soft vicinity function      270
Soft-margin separating hyperplane      135
Spline function: with a finite number of nodes      194
Spline function: with an infinite number of nodes      195
Stochastic approximation stopping rule      33
Stochastic ill-posed problems      113
Strong mode estimating a probability measure      63
Structural risk minimization principle      94
Structure      94
Structure of growth function      79
Supervisor      17
Support vector ANOVA decomposition      199
Support vector machines      138
Support vectors      134
SVM conditional density estimator      258
SVM conditional probability estimator      255
SVM density estimator      247
Tails of distribution      77
Tangent distance      150
Training set      18
Transductive inference      293
Turing — Church thesis      177
Two layer neural networks machine      145
Two-sided empirical process      46
U.S. Postal Service digit database      173
Uniform one-sided convergence      39
Uniform two-sided convergence      39
VC dimension of a set of indicator functions      79
VC dimension of a set of real functions      81
VC entropy      44
VC subgraph      90
Vicinal risk minimization method      267
Vicinity kernel      273
Vicinity kernel: one-vicinal kernel      273
Vicinity kernel: two-vicinal kernel      273
VRM method for conditional density estimation      286
VRM method for conditional probability estimation      285
VRM method for density estimation      284
VRM method for pattern recognition      273
VRM method for regression estimation      287
Weak mode estimating a probability measure      63
Weight decay procedure      102

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