Optimal exponential bounds on the accuracy of classification

DOI10.1007/s00365-014-9229-3zbMath1304.62056OpenAlexW2187047180MaRDI QIDQ485316

Vladimir I. Koltchinskii, Alexandre B. Tsybakov, Dominique Picard, Vladimir N. Temlyakov, Gérard Kerkyacharian

Publication date: 9 January 2015

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: http://crest.science/RePEc/wpstorage/2013-39.pdf

zbMATH Keywords

classificationBahadur efficiencyoptimal rate of convergencestatistical learningfast ratesmargin conditionexcess risk

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Pattern recognition, speech recognition (68T10)

Related Items

A minimax framework for quantifying risk-fairness trade-off in regression

Cites Work

• Unnamed Item
• Unnamed Item
• Oracle inequalities in empirical risk minimization and sparse recovery problems. École d'Été de Probabilités de Saint-Flour XXXVIII-2008.
• 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
• Optimal aggregation of classifiers in statistical learning.
• Weak convergence and empirical processes. With applications to statistics
• Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)
• Approximation methods for supervised learning
• Approximation in learning theory
• Square root penalty: Adaption to the margin in classification and in edge estimation
• Uniform Central Limit Theorems
• Minimax nonparametric classification .I. Rates of convergence
• 10.1162/1532443041424319
• Convexity, Classification, and Risk Bounds
• Introduction to nonparametric estimation