Grouped variable selection with discrete optimization: computational and statistical perspectives

DOI10.1214/21-aos2155arXiv2104.07084OpenAlexW3153278865MaRDI QIDQ6046300

Rahul Mazumder, Hussein Hazimeh, Peter Radchenko

Publication date: 10 May 2023

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

Full work available at URL: https://arxiv.org/abs/2104.07084

zbMATH Keywords

mixed integer programmingbranch and bound algorithmssparsity\(\ell_0\) regularizationgroup variable selectionnonparametric additive models

Mathematics Subject Classification ID

Linear inference, regression (62Jxx) Nonparametric estimation (62G05) Large-scale problems in mathematical programming (90C06) Mixed integer programming (90C11)

Related Items

Best subset selection with shrinkage: sparse additive hazards regression with the grouping effect

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nearly unbiased variable selection under minimax concave penalty
• Best subset selection via a modern optimization lens
• Fast learning rate of multiple kernel learning: trade-off between sparsity and smoothness
• Iterative hard thresholding methods for \(l_0\) regularized convex cone programming
• Minimax optimal rates of estimation in high dimensional additive models
• Optimal prediction for sparse linear models? Lower bounds for coordinate-separable M-estimators
• Statistics for high-dimensional data. Methods, theory and applications.
• Sparsity in multiple kernel learning
• Consistent group selection in high-dimensional linear regression
• Oracle inequalities and optimal inference under group sparsity
• Some theoretical results on the grouped variables Lasso
• Iterative thresholding for sparse approximations
• Factor-driven two-regime regression
• Component selection and smoothing in multivariate nonparametric regression
• The sparsity and bias of the LASSO selection in high-dimensional linear regression
• The benefit of group sparsity
• Variable selection in nonparametric additive models
• Algorithms for simultaneous sparse approximation. II: Convex relaxation
• High-dimensional additive modeling
• The composite absolute penalties family for grouped and hierarchical variable selection
• Branch-and-bound algorithms: a survey of recent advances in searching, branching, and pruning
• On the best search strategy in parallel branch-and-bound: Best-first search versus lazy depth-first search
• A brief history of linear and mixed-integer programming computation
• On the asymptotic properties of the group lasso estimator for linear models
• Sparse regression at scale: branch-and-bound rooted in first-order optimization
• Sparse high-dimensional regression: exact scalable algorithms and phase transitions
• Sparse HP filter: finding kinks in the COVID-19 contact rate
• Doubly penalized estimation in additive regression with high-dimensional data
• Support union recovery in high-dimensional multivariate regression
• Calibrating nonconvex penalized regression in ultra-high dimension
• Perspective cuts for a class of convex 0-1 mixed integer programs
• Perspective reformulations of mixed integer nonlinear programs with indicator variables
• Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms
• SparseNet: Coordinate Descent With Nonconvex Penalties
• On the Reconstruction of Block-Sparse Signals With an Optimal Number of Measurements
• Theoretical Results on Sparse Representations of Multiple-Measurement Vectors
• Sparse Additive Models
• Sparse Approximate Solutions to Linear Systems
• Using ℓ1-Relaxation and Integer Programming to Obtain Dual Bounds for Sparse PCA
• Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms
• Scalable Algorithms for the Sparse Ridge Regression
• Variable Selection Using Adaptive Nonlinear Interaction Structures in High Dimensions
• Theoretical and Empirical Results for Recovery From Multiple Measurements
• The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimization
• Sparse solutions to linear inverse problems with multiple measurement vectors
• A sparse signal reconstruction perspective for source localization with sensor arrays
• Minimax-optimal rates for sparse additive models over kernel classes via convex programming
• On the Convergence of Block Coordinate Descent Type Methods
• Mixed-integer nonlinear optimization
• Model Selection and Estimation in Regression with Grouped Variables
• Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors
• Structured sparsity through convex optimization
• A selective review of group selection in high-dimensional models