Accuracy guaranties for \(\ell_{1}\) recovery of block-sparse signals

DOI10.1214/12-AOS1057zbMath1296.62088arXiv1111.2546WikidataQ57392890 ScholiaQ57392890MaRDI QIDQ741817

Arkadi Nemirovski, Anatoli B. Juditsky, Boris T. Polyak, Fatma Kılınç-Karzan

Publication date: 15 September 2014

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

Full work available at URL: https://arxiv.org/abs/1111.2546

zbMATH Keywords

oracle inequalitiessparse recoverynonparametric estimation by convex optimization

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Estimation in multivariate analysis (62H12) Applications of mathematical programming (90C90)

Related Items

Parameter choices for sparse regularization with the ℓ1 norm ^*, On asymptotically optimal confidence regions and tests for high-dimensional models, High-order evaluation complexity for convexly-constrained optimization with non-Lipschitzian group sparsity terms, Group Sparse Optimization for Images Recovery Using Capped Folded Concave Functions

Cites Work

• Unnamed Item
• On verifiable sufficient conditions for sparse signal recovery via \(\ell_{1}\) minimization
• Verifiable conditions of \(\ell_{1}\)-recovery for sparse signals with sign restrictions
• Oracle inequalities and optimal inference under group sparsity
• Some theoretical results on the grouped variables Lasso
• The restricted isometry property and its implications for compressed sensing
• The benefit of group sparsity
• On the asymptotic properties of the group lasso estimator for linear models
• On the conditions used to prove oracle results for the Lasso
• Simultaneous analysis of Lasso and Dantzig selector
• Support union recovery in high-dimensional multivariate regression
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• On Low Rank Matrix Approximations with Applications to Synthesis Problem in Compressed Sensing
• Decoding by Linear Programming
• Stable recovery of sparse overcomplete representations in the presence of noise
• Sparse representations in unions of bases
• DASSO: Connections Between the Dantzig Selector and Lasso
• The Group Lasso for Logistic Regression
• On the Reconstruction of Block-Sparse Signals With an Optimal Number of Measurements
• Block-Sparse Signals: Uncertainty Relations and Efficient Recovery
• Robust Recovery of Signals From a Structured Union of Subspaces
• Accuracy Guarantees for <formula formulatype="inline"> <tex Notation="TeX">$\ell_1$</tex></formula>-Recovery
• Model-Based Compressive Sensing
• The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing
• Model Selection and Estimation in Regression with Grouped Variables