PAC-Bayesian estimation and prediction in sparse additive models

DOI10.1214/13-EJS771zbMath1337.62075arXiv1208.1211OpenAlexW3102208618MaRDI QIDQ1951111

Pierre Alquier, Benjamin Guedj

Publication date: 29 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.1211

zbMATH Keywords

additive modelsregression estimationsparsitystochastic searchMCMCoracle inequalityPAC-Bayesian bounds

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Ridge regression; shrinkage estimators (Lasso) (62J07) General nonlinear regression (62J02) Numerical analysis or methods applied to Markov chains (65C40)

Related Items (11)

Simpler PAC-Bayesian bounds for hostile data ⋮ PAC-Bayesian high dimensional bipartite ranking ⋮ An oracle inequality for quasi-Bayesian nonnegative matrix factorization ⋮ User-friendly Introduction to PAC-Bayes Bounds ⋮ Bayesian fractional posteriors ⋮ On some recent advances on high dimensional Bayesian statistics ⋮ A quasi-Bayesian perspective to online clustering ⋮ On oracle property and asymptotic validity of Bayesian generalized method of moments ⋮ On the exponentially weighted aggregate with the Laplace prior ⋮ Sharp oracle inequalities for low-complexity priors ⋮ Sampling from non-smooth distributions through Langevin diffusion

Uses Software

• R
• SSS
• pacbpred
• ElemStatLearn
• hgam

Cites Work

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• Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
• Graph Selection with GGMselect
• Fast learning rate of multiple kernel learning: trade-off between sparsity and smoothness
• Sparse regression learning by aggregation and Langevin Monte-Carlo
• Statistics for high-dimensional data. Methods, theory and applications.
• Sparsity in multiple kernel learning
• Robust linear least squares regression
• PAC-Bayesian bounds for randomized empirical risk minimizers
• Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
• Lasso-type recovery of sparse representations for high-dimensional data
• High-dimensional additive modeling
• Additive regression and other nonparametric models
• Generalized additive models
• Statistical learning theory and stochastic optimization. Ecole d'Eté de Probabilitiés de Saint-Flour XXXI -- 2001.
• Aggregated estimators and empirical complexity for least square regression
• PAC-Bayesian bounds for sparse regression estimation with exponential weights
• Some PAC-Bayesian theorems
• Fast learning rates in statistical inference through aggregation
• Simultaneous analysis of Lasso and Dantzig selector
• High-dimensional generalized linear models and the lasso
• Markov Chains and Stochastic Stability
• Aggregation and Sparsity Via ℓ1 Penalized Least Squares
• Shotgun Stochastic Search for “Largep” Regression
• Minimax-optimal rates for sparse additive models over kernel classes via convex programming
• Sparse single-index model
• Introduction to nonparametric estimation
• Sparse estimation by exponential weighting

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