A look at robustness and stability of \(\ell_1\)-versus \(\ell_0\)-regularization: discussion of papers by Bertsimas et al. and Hastie et al.

DOI10.1214/20-STS809OpenAlexW3098688965MaRDI QIDQ2225318

Armeen Taeb, Yuansi Chen, Peter Bühlmann

Publication date: 8 February 2021

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ss/1605603635

zbMATH Keywords

latent variablesvariable selectiondistributional robustnesshigh-dimensional estimationlow-rank estimation

Mathematics Subject Classification ID

Statistics (62-XX)

Related Items (2)

A literature review of (Sparse) exponential family PCA ⋮ Rejoinder: ``Sparse regression: scalable algorithms and empirical performance

Uses Software

• SDPLR
• PDCO
• glmnet
• ElemStatLearn
• TensorFlow
• PyTorch
• LZeroSpikeInference

Cites Work

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• Bagging predictors
• The Adaptive Lasso and Its Oracle Properties
• Exact Spike Train Inference Via $\ell_0$ Optimization
• Best subset selection via a modern optimization lens
• \(\ell_{0}\)-penalized maximum likelihood for sparse directed acyclic graphs
• Statistics for high-dimensional data. Methods, theory and applications.
• Characterization of the equivalence of robustification and regularization in linear and matrix regression
• Algorithm for cardinality-constrained quadratic optimization
• Efficient algorithms for computing the best subset regression models for large-scale problems
• Relaxed Lasso
• Breakthroughs in statistics. Volume I: Foundations and basic theory
• Estimating the dimension of a model
• Risk bounds for model selection via penalization
• Heuristics of instability and stabilization in model selection
• A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
• Statistics for big data: a perspective
• Logistic regression: from art to science
• Least angle regression. (With discussion)
• On the conditions used to prove oracle results for the Lasso
• The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso)
• Sparse high-dimensional regression: exact scalable algorithms and phase transitions
• Simultaneous analysis of Lasso and Dantzig selector
• Boosting for high-dimensional linear models
• Atomic Decomposition by Basis Pursuit
• Better Subset Regression Using the Nonnegative Garrote
• On Sparse Representations in Arbitrary Redundant Bases
• Greed is Good: Algorithmic Results for Sparse Approximation
• 10.1162/153244303321897717
• Matching pursuits with time-frequency dictionaries
• Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$-Constrained Quadratic Programming (Lasso)
• Sparse Recovery With Orthogonal Matching Pursuit Under RIP
• Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise
• Robust Regression and Lasso
• Regularization and Variable Selection Via the Elastic Net
• Certifiably Optimal Low Rank Factor Analysis
• For most large underdetermined systems of linear equations the minimal 𝓁₁‐norm solution is also the sparsest solution

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