Aggregation by Exponential Weighting and Sharp Oracle Inequalities

DOI10.1007/978-3-540-72927-3_9zbMATH Open1203.62063OpenAlexW1509060282MaRDI QIDQ5432428

Arnak S. Dalalyan, A. B. Tsybakov

Publication date: 3 January 2008

Published in: Learning Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-72927-3_9

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08)

Related Items (37)

Mixing partially linear regression models ⋮ Exponential weights in multivariate regression and a low-rankness favoring prior ⋮ An oracle inequality for quasi-Bayesian nonnegative matrix factorization ⋮ Exponential weighting and oracle inequalities for projection estimates ⋮ Bayesian linear regression with sparse priors ⋮ Non-local methods with shape-adaptive patches (NLM-SAP) ⋮ PAC-Bayesian risk bounds for group-analysis sparse regression by exponential weighting ⋮ Sharp oracle inequalities for aggregation of affine estimators ⋮ Aggregation of estimators and stochastic optimization ⋮ On the optimality of the empirical risk minimization procedure for the convex aggregation problem ⋮ Simple proof of the risk bound for denoising by exponential weights for asymmetric noise distributions ⋮ Minimax risks for sparse regressions: ultra-high dimensional phenomenons ⋮ Optimal model selection in heteroscedastic regression using piecewise polynomial functions ⋮ Sparse regression learning by aggregation and Langevin Monte-Carlo ⋮ On \(\beta\)-precision aggregation. ⋮ PAC-Bayesian bounds for sparse regression estimation with exponential weights ⋮ The smooth-Lasso and other \(\ell _{1}+\ell _{2}\)-penalized methods ⋮ On the optimality of the aggregate with exponential weights for low temperatures ⋮ Mirror averaging with sparsity priors ⋮ Transductive versions of the Lasso and the Dantzig selector ⋮ Kullback-Leibler aggregation and misspecified generalized linear models ⋮ Generalization of constraints for high dimensional regression problems ⋮ Aggregation of affine estimators ⋮ Estimation and variable selection with exponential weights ⋮ Optimal learning with \textit{Q}-aggregation ⋮ Deviation optimal learning using greedy \(Q\)-aggregation ⋮ Exponential screening and optimal rates of sparse estimation ⋮ Prediction error bounds for linear regression with the TREX ⋮ A quasi-Bayesian perspective to online clustering ⋮ Sparse estimation by exponential weighting ⋮ Some theoretical results on the grouped variables Lasso ⋮ On the exponentially weighted aggregate with the Laplace prior ⋮ Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity ⋮ Sharp oracle inequalities for low-complexity priors ⋮ Sparse recovery in convex hulls via entropy penalization ⋮ Sampling from non-smooth distributions through Langevin diffusion ⋮ Localized Gaussian width of \(M\)-convex hulls with applications to Lasso and convex aggregation

Recommendations

• Concentration inequalities for the exponential weighting method 👍 👎
• Optimal exponential bounds for aggregation of density estimators 👍 👎
• Exponential inequalities for weighted sums of bounded random variables 👍 👎
• Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity 👍 👎
• Exponential weighting and oracle inequalities for projection estimates 👍 👎
• Sharp oracle inequalities for aggregation of affine estimators 👍 👎
• Aggregating estimates by convex optimization 👍 👎
• Optimal exponential bounds for aggregation of estimators for the Kullback-Leibler loss 👍 👎
• A weighted and exponential generalization of Wilker's inequality and its applications 👍 👎
• Sharp oracle bounds for monotone and convex regression through aggregation 👍 👎

This page was built for publication: Aggregation by Exponential Weighting and Sharp Oracle Inequalities

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5432428)