Simultaneous adaptation to the margin and to complexity in classification

DOI10.1214/009053607000000055zbMath1209.62146arXivmath/0509696OpenAlexW1981292117MaRDI QIDQ2456017

Guillaume Lecué

Publication date: 17 October 2007

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509696

zbMATH Keywords

classificationaggregationstatistical learningSVMmarginfast rates of convergenceexcess riskcomplexity of classes of sets

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Pattern recognition, speech recognition (68T10)

Related Items

Classification in general finite dimensional spaces with the \(k\)-nearest neighbor rule, Fast learning rates in statistical inference through aggregation, Ordered smoothers with exponential weighting, PAC-Bayesian risk bounds for group-analysis sparse regression by exponential weighting, Statistical performance of support vector machines, Risk bounds for CART classifiers under a margin condition, On the optimality of the aggregate with exponential weights for low temperatures, Kullback-Leibler aggregation and misspecified generalized linear models, Margin-adaptive model selection in statistical learning, Concentration inequalities for the exponential weighting method, Optimal rates of aggregation in classification under low noise assumption, Sparse estimation by exponential weighting, A universal procedure for aggregating estimators, Bandwidth selection in kernel empirical risk minimization via the gradient, Set structured global empirical risk minimizers are rate optimal in general dimensions, Sharp oracle inequalities for low-complexity priors, Sampling from non-smooth distributions through Langevin diffusion

Uses Software

• AdaBoost.MH

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minimax theory of image reconstruction
• Risk bounds for statistical learning
• Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
• Fast rates for support vector machines using Gaussian kernels
• Fast learning rates for plug-in classifiers
• A decision-theoretic generalization of on-line learning and an application to boosting
• Combining different procedures for adaptive regression
• Smooth discrimination analysis
• Boosting the margin: a new explanation for the effectiveness of voting methods
• Mixing strategies for density estimation.
• Additive logistic regression: a statistical view of boosting. (With discussion and a rejoinder by the authors)
• Functional aggregation for nonparametric regression.
• Analyzing bagging
• Complexity regularization via localized random penalties
• Statistical learning theory and stochastic optimization. Ecole d'Eté de Probabilitiés de Saint-Flour XXXI -- 2001.
• On the Bayes-risk consistency of regularized boosting methods.
• Statistical behavior and consistency of classification methods based on convex risk minimization.
• Optimal aggregation of classifiers in statistical learning.
• Asymptotical minimax recovery of sets with smooth boundaries
• Support-vector networks
• Metric entropy of some classes of sets with differentiable boundaries
• Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)
• Statistical performance of support vector machines
• Recursive aggregation of estimators by the mirror descent algorithm with averaging
• Aggregation for Gaussian regression
• Model selection via testing: an alternative to (penalized) maximum likelihood estimators.
• Square root penalty: Adaption to the margin in classification and in edge estimation
• Classifiers of support vector machine type with \(\ell_1\) complexity regularization
• Theory of Classification: a Survey of Some Recent Advances
• Information Theory and Mixing Least-Squares Regressions
• Sequential Procedures for Aggregating Arbitrary Estimators of a Conditional Mean
• Model Selection: An Integral Part of Inference
• Rademacher penalties and structural risk minimization
• 10.1162/1532443041424319
• Learning Theory and Kernel Machines
• Prediction, Learning, and Games
• Learning Theory
• Convexity, Classification, and Risk Bounds
• Some applications of concentration inequalities to statistics