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|a (JST)25463570
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|a eng
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|a 62G07
|2 MSC
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|2 MSC
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|2 MSC
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|a 68T10
|2 MSC
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|a Audibert, Jean-Yves
|e verfasserin
|4 aut
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|a Fast Learning Rates for Plug-In Classifiers
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|c 2007
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|a Text
|b txt
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|a Computermedien
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|a Online-Ressource
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|a It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than $n^{-1/2}$. The work on this subject has suggested the following two conjectures: (i) the best achievable fast rate is of the order n⁻¹, and (ii) the plug-in classifiers generally converge more slowly than the classifiers based on empirical risk minimization. We show that both conjectures are not correct. In particular, we construct plug-in classifiers that can achieve not only fast, but also super-fast rates, that is, rates faster than n⁻¹. We establish minimax lower bounds showing that the obtained rates cannot be improved.
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|a Copyright 2007 Institute of Mathematical Statistics
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|a Classification
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|a Statistical learning
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|a Fast rates of convergence
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|a Excess risk
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|a Plug-in classifiers
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|a Minimax lower bounds
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Inferential statistics
|x Statistical estimation
|x Estimation methods
|x Estimators
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|
4 |
|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Learning
|x Learning rate
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650 |
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4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
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650 |
|
4 |
|a Mathematics
|x Mathematical expressions
|x Mathematical functions
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650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Algebra
|x Polynomials
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|
4 |
|a Mathematics
|x Applied mathematics
|x Game theory
|x Minimax
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|
4 |
|a Physical sciences
|x Physics
|x Mechanics
|x Density
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|
4 |
|a Applied sciences
|x Computer science
|x Artificial intelligence
|x Machine learning
|x Perceptron convergence procedure
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650 |
|
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|a Mathematics
|x Pure mathematics
|x Discrete mathematics
|x Number theory
|x Numbers
|x Real numbers
|x Rational numbers
|x Integers
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650 |
|
4 |
|a Mathematics
|x Mathematical analysis
|x Measure theory
|x Lebesgue measures
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650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Inferential statistics
|x Statistical estimation
|x Estimation methods
|x Estimators
|
650 |
|
4 |
|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Learning
|x Learning rate
|
650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
|
650 |
|
4 |
|a Mathematics
|x Mathematical expressions
|x Mathematical functions
|
650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Algebra
|x Polynomials
|
650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Game theory
|x Minimax
|
650 |
|
4 |
|a Physical sciences
|x Physics
|x Mechanics
|x Density
|
650 |
|
4 |
|a Applied sciences
|x Computer science
|x Artificial intelligence
|x Machine learning
|x Perceptron convergence procedure
|
650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Discrete mathematics
|x Number theory
|x Numbers
|x Real numbers
|x Rational numbers
|x Integers
|
650 |
|
4 |
|a Mathematics
|x Mathematical analysis
|x Measure theory
|x Lebesgue measures
|x Statistical Learning Theory
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|
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|a research-article
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1 |
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|a Tsybakov, Alexandre B.
|e verfasserin
|4 aut
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0 |
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|i Enthalten in
|t The Annals of Statistics
|d Institute of Mathematical Statistics
|g 35(2007), 2, Seite 608-633
|w (DE-627)270129162
|w (DE-600)1476670-X
|x 00905364
|7 nnns
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1 |
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|g volume:35
|g year:2007
|g number:2
|g pages:608-633
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|u https://www.jstor.org/stable/25463570
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|d 35
|j 2007
|e 2
|h 608-633
|