On model selection consistency of regularized M-estimators

DOI10.1214/15-EJS1013zbMath1309.62044arXiv1305.7477MaRDI QIDQ2340872

Jonathan E. Taylor, Jason D. Lee, Yuekai Sun

Publication date: 21 April 2015

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

Full work available at URL: https://arxiv.org/abs/1305.7477

zbMATH Keywords

group lassolassonuclear norm minimizationgeneralized lassogeometrically decomposable penaltiesregularized M-estimator

Mathematics Subject Classification ID

Point estimation (62F10)

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Uses Software

• PDCO
• glasso

Cites Work

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• Sparse inverse covariance estimation with the graphical lasso
• Latent variable graphical model selection via convex optimization
• Simple bounds for recovering low-complexity models
• Statistics for high-dimensional data. Methods, theory and applications.
• Estimation of (near) low-rank matrices with noise and high-dimensional scaling
• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• The solution path of the generalized lasso
• High-dimensional Ising model selection using \(\ell _{1}\)-regularized logistic regression
• Estimating time-varying networks
• The convex geometry of linear inverse problems
• Honest variable selection in linear and logistic regression models via \(\ell _{1}\) and \(\ell _{1}+\ell _{2}\) penalization
• High-dimensional covariance estimation by minimizing \(\ell _{1}\)-penalized log-determinant divergence
• Local behavior of sparse analysis regularization: applications to risk estimation
• Support union recovery in high-dimensional multivariate regression
• Structure estimation for discrete graphical models: generalized covariance matrices and their inverses
• High-dimensional graphs and variable selection with the Lasso
• Atomic Decomposition by Basis Pursuit
• Reconstruction From Anisotropic Random Measurements
• Graphical Models, Exponential Families, and Variational Inference
• Perturbation Bounds of Unitary and Subunitary Polar Factors
• Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$-Constrained Quadratic Programming (Lasso)
• Weakly decomposable regularization penalties and structured sparsity
• A unified framework for high-dimensional analysis of \(M\)-estimators with decomposable regularizers