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Theory of Classification: a Survey of Some Recent Advances (Q3373749)

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Language	Label	Description	Also known as
English	Theory of Classification: a Survey of Some Recent Advances	scientific article

Statements

scholarly article

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Theory of Classification: a Survey of Some Recent Advances (English)

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zbMATH Open document ID

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10.1051/ps:2005018

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Stéphane Boucheron

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Olivier Bousquet

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ESAIM: Probability and Statistics

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publication date

9 March 2006

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full work available at URL

http://www.numdam.org/item?id=PS_2005__9__323_0

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https://eudml.org/doc/244764

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

Pattern recognition

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statistical learning theory

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concentration inequalities

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empirical processes

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model selection

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Correction to bounds on conditional probabilities with applications

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The method of potential functions for the problem of restoring the characteristic of a function converter from randomly observed points

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The probability problem of pattern recognition learning and the method of potential functions

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Theoretical foundations of the potential function method in pattern recognition learning

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A new look at the statistical model identification

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A Remark on the Szarek–Talagrand Theorem

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Scale-sensitive dimensions, uniform convergence, and learnability

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Neural Network Learning

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A result of Vapnik with applications

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10.1162/153244303768966111

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Strong minimax lower bounds for learning

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Density and dimension

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Weighted sums of certain dependent random variables

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Model selection for regression on a fixed design

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Risk bounds for model selection via penalization

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Minimum complexity density estimation

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Model selection and error estimation

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Local Rademacher complexities

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Hardness results for neural network approximation problems

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Convexity, Classification, and Risk Bounds

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10.1162/153244303321897690

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Learning Theory

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Potential function algorithms for pattern recognition learning machines

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10.1162/153244303321897681

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Probability Inequalities for the Sum of Independent Random Variables

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An alternative point of view on Lepski's method

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Rates of convergence for minimum contrast estimators

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Minimum contrast estimators on sieves: Exponential bounds and rates of convergence

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Statistical performance of support vector machines

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10.1162/1532443041424319

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Learnability and the Vapnik-Chervonenkis dimension

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Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution

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Moment inequalities for functions of independent random variables

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A sharp concentration inequality with applications

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Concentration inequalities using the entropy method

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A Bennett concentration inequality and its application to suprema of empirical processes

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10.1162/153244302760200704

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Arcing classifiers. (With discussion)

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Population theory for boosting ensembles.

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Boosting With the<i>L</i><sub>2</sub>Loss

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10.1162/153244302760200650

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Density estimation via exponential model selection

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Statistical learning theory and stochastic optimization. Ecole d'Eté de Probabilitiés de Saint-Flour XXXI -- 2001.

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A graph-theoretic generalization of the Sauer-Shelah lemma

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Logistic regression, AdaBoost and Bregman distances

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Support-vector networks

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Enumeration of Seven-Argument Threshold Functions

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Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation

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Large-scale typicality of Markov sample paths and consistency of MDL order estimators

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The consistency of the BIC Markov order estimator.

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On the mathematical foundations of learning

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Information inequalities and concentration of measure

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Automatic pattern recognition: a study of the probability of error

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Distribution-free inequalities for the deleted and holdout error estimates

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Distribution-free performance bounds for potential function rules

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Ideal spatial adaptation by wavelet shrinkage

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Central limit theorems for empirical measures

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Balls in \(\mathbb{R}^k\) do not cut all subsets of \(k+2\) points

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Universal Donsker classes and metric entropy

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Uniform Central Limit Theorems

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Uniform and universal Glivenko-Cantelli classes

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Bootstrap methods: another look at the jackknife

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A general lower bound on the number of examples needed for learning

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Regularization networks and support vector machines

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On the trace of finite sets

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Boosting a weak learning algorithm by majority

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Generalization bounds for averaged classifiers

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A decision-theoretic generalization of on-line learning and an application to boosting

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Additive logistic regression: a statistical view of boosting. (With discussion and a rejoinder by the authors)

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Empirical processes and applications: An overview. (With discussion)

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Some limit theorems for empirical processes (with discussion)

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Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers

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Large sample optimality of least squares cross-validation in density estimation

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The elements of statistical learning. Data mining, inference, and prediction

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Decision theoretic generalizations of the PAC model for neural net and other learning applications

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Sphere packing numbers for subsets of the Boolean \(n\)-cube with bounded Vapnik-Chervonenkis dimension

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Predicting \(\{ 0,1\}\)-functions on randomly drawn points

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10.1162/153244303765208368

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Probability Inequalities for Sums of Bounded Random Variables

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Process consistency for AdaBoost.

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The densest hemisphere problem

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Behavioral and prescriptive explanations of a reverse sunk cost effect

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Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks

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Strongly consistent code-based identification and order estimation for constrained finite-state model classes

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A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines

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Neural networks with quadratic VC dimension

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Rademacher penalties and structural risk minimization

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Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)

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Empirical margin distributions and bounding the generalization error of combined classifiers

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Learning pattern classification-a survey

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On Talagrand's deviation inequalities for product measures

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The importance of convexity in learning with squared loss

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Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors

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Improved bounds on the sample complexity of learning

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A note on margin-based loss functions in classification

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Concentration for locally acting permutations

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Adaptive model selection using empirical complexities

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On the Bayes-risk consistency of regularized boosting methods.

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Complexity regularization via localized random penalties

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Concept learning using complexity regularization

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Finiteness results for sigmoidal “neural” networks

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Some Comments on C P

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Smooth discrimination analysis

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A simple proof of the blowing-up lemma (Corresp.)

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Bounding \(\bar d\)-distance by informational divergence: A method to prove measure concentration

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Erratum to: ``A measure concentration inequality for contracting Markov chains''

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About the constants in Talagrand's concentration inequalities for empirical processes.

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Some applications of concentration inequalities to statistics

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Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.

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Risk bounds for statistical learning

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PAC-Bayesian stochastic model selection

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Concentration for Independent Permutations

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Improving the sample complexity using global data

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Entropy and the combinatorial dimension

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Probably Approximate Learning of Sets and Functions

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A note on Talagrand's concentration inequality

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Some extensions of an inequality of Vapnik and Chervonenkis

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Symmetrization approach to concentration inequalities for empirical processes.

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Convergence of stochastic processes

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Measuring mass concentrations and estimating density contour clusters -- An excess mass approach

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Concentration inequalities for set-indexed empirical processes

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Une inégalité de Bennett pour les maxima de processus empiriques. (A Bennet type inequality for maxima of empirical processes)

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A finite sample distribution-free performance bound for local discrimination rules

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Combinatorics of random processes and sections of convex bodies

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On the density of families of sets

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Boosting the margin: a new explanation for the effectiveness of voting methods

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Learning Theory

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PAC-Bayesian Generalisation Error Bounds for Gaussian Process Classification

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Structural risk minimization over data-dependent hierarchies

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A combinatorial problem; stability and order for models and theories in infinitary languages

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Existence of submatrices with all possible columns

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10.1162/153244302760185252

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Consistency of Support Vector Machines and Other Regularized Kernel Classifiers

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Support vector machines are universally consistent

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10.1162/1532443041827925

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On the convexified Sauer-Shelah theorem

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The Glivenko-Cantelli problem

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Sharper bounds for Gaussian and empirical processes

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Concentration of measure and isoperimetric inequalities in product spaces

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The Glivenko-Cantelli problem, ten years later

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Majorizing measures: The generic chaining

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New concentration inequalities in product spaces

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A new look at independence

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Vapnik-Chervonenkis type conditions and uniform Donsker classes of functions

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The Generic Chaining

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On nonparametric estimation of density level sets

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Optimal aggregation of classifiers in statistical learning.

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Introduction to nonparametric estimation

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Square root penalty: Adaption to the margin in classification and in edge estimation

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A new approach to least-squares estimation, with applications

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Estimating a regression function

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Weak convergence and empirical processes. With applications to statistics

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Estimation of dependences based on empirical data. Transl. from the Russian by Samuel Kotz

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On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities

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Necessary and Sufficient Conditions for the Uniform Convergence of Means to their Expectations

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On the infeasibility of training neural networks with small mean-squared error

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Model selection in nonparametric regression

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Some special Vapnik-Chervonenkis classes

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Minimax nonparametric classification .I. Rates of convergence

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Minimax nonparametric classification. II. Model selection for adaptation

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Exponential Bounds for Large Deviations

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Exponential inequalities for sums of random vectors

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Statistical behavior and consistency of classification methods based on convex risk minimization.

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Capacity of reproducing kernel spaces in learning theory

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Mathematics(1 entry)

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