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Vapnik V. — Estimation of dependences based on empirical data
Vapnik V. — Estimation of dependences based on empirical data

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Название: Estimation of dependences based on empirical data

Автор: Vapnik V.

Аннотация:

Estimating dependences on the basis of empirical data has been, and will probably remain, a central problem in applied analysis. This problem is a mathematical interpretation of one of the basic questions of science: how to extract the existing law-like relationship from scattered data.
The simplest attack on this problem is to construct (estimate) a function from its values at certain points. Here we will formulate some general principles of estimating a functional dependence, and then develop an algorithm for the estimation using these principles.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 299

Добавлена в каталог: 10.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_{p}^{2}$ metric      192 194 259
Accuracy      14
Algorithm, general      368
Algorithm, special      366
Baranchik theorem      120
Bayes's formula      47 52 60 67 366
Bayes's principle      51 128
Bernoulli theorem      162
Bhattacharya's theorem      118
Borel — Cantelli lemma      270 284
C metric      192 194
Canonical, space      211
Canonical, structure      211
Capacity characteristics      147 152
Cauchy — Schwarz inequality      95 188
Chebyshev inequality      31 32 279 284
Class of correctness      22
Closeness of function      15 16
Closeness of function in the $L_{p}^{2}$ metric      16 17 18
Closeness of function in the C metric      16 17 18
Complete sample      345
Completely continuous linear operator      21
Confidence      14
Conjugate gradients, method of      359 360
Conjugations      288
Correctness in Tihonov's sense      22 23
Covering by a finite net      149
Density, formed by a mixture      106
Density, nondegenerate at 0      100 106
Density, robust in a class      95
Density, with a bounded variance      99 106
Dichotomies      330 331
Dirichlet kernels      296
Distribution, binomial      343
Distribution, double exponential      33
Distribution, Gaussian      33 34 56 57 59 70 84 87 91 99 101 103
Distribution, Laplace      33 34 84 85 87 90 91 99 101 103
Distribution, Poisson      122 123
Distribution, uniform      33 34 84
Distribution, Wishart      59 60 62 68 69 244 245
Dual problem      356
Empirical function      27
Empirical mean      40
Empirical mean, convergence of      40
entropy      152 153 365
Entropy, mean      365
Equivalence classes      316 321 323 343 345
Estimating derivatives      13 291
Estimator, asymptotically efficient      75
Estimator, asymptotically unbiased      75
Estimator, Bayesian      71
Estimator, consistent      74
Estimator, jointly efficient      73
Estimator, linear minimax      71
Estimator, minimax      71
Estimator, of Stein-type      79
Estimator, ridge regression      122 239
Experiment      7
Experiment, closed      7
Experiment, open      7
Extreme vector      356
Fisher matrix      113
Fisher's information quantity      72 96
Fourier transform      302 303
Fredholm integral equation      10 13 66 75 289
Functional of empirical risk      35 39
Gauss — Markov model      112 114 115
Glivenko — Cantelli theorem      37 38 41 42 155 305
Hoeffding inequality      31
Identifying linear objects      12
Inverse problem of gravimetry      290
Inverse problem of spectroscopy      11
James — Stein theorem      116
Kolmogorov — Smirnov bound      293
Koshcheev theorems      130 136
Kronecker symbol      373
Kuhn — Tucker theorem      355 356
Lagrange function      see “Lagrange multipliers”
Lagrange multipliers      77 88 198 200 201 260
Linear discriminant analysis      47 48
Lipschitz condition      294 298 299
Loss function      2 183
Loss function, quadratic      141 183
Lozinskii — Kharshiladze theorem      286
Method of minimal modules      86
Mihalskii theorem      287
Minimax principle      52
Nadaraya's result      302
Newton's binomial expansion      167
Nonparametric statistics      39
Normal distribution      see “Gaussian distribution”
Nuclear spectroscopy      289
Operator equation      10
Operator equation, stable      10
Operator equation, well-posed in the Hadamard sense      10 21
Parametric statistics      39
Prior information      29 34 134
Proper $\varepsilon$-net      207
Quadratic form      245
Rao — Cramer inequality      71 72 113
Regularization parameter      24
Relative variance of losses      183 184
Sequential search procedure      360
Set of correctness      22
Smirnov formula      299
Spline approximation      286 289
Splines, canonical      288 373
Stabilizer      23
Structure      234 236
Structure, combined      260
Tanimoto's metric      350
Taxon      347
Taxonomic structure      333-336
Tihonov's theorems      308
Training sample      313 346
Training sequence      3 328 333
Variance      30
Variance, absolute bound on      30
Variance, relative value      30
Volterra integral equation      13
Wiener — Hopf equation      12
Working sample      313 329 333 338 341 346
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