Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors

2012/09/30 by Patrick Breheny, Jian Huang · 9 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Face and Expression Recognition #Statistical Methods and Inference #stat.CO #stat.ML

paper · pdf · doi:10.1007/s11222-013-9424-2

published as Statistics and Computing, 25: 173-187 (2015)

arxiv created 2013/08/23 · openalex publication_date 2013/11/04 · openalex created_date 2016/06/24 · arxiv updated 2016/07/20 · openalex updated_date 2026/07/29

Abstract

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group selection. Nonconvex penalties such as SCAD and MCP have been proposed and shown to have several advantages over the lasso; these penalties may also be extended to the group selection problem, giving rise to group SCAD and group MCP methods. Here, we describe algorithms for fitting these models stably and efficiently. In addition, we present simulation results and real data examples comparing and contrasting the statistical properties of these methods.

Citations

• Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization
• Nearly unbiased variable selection under minimax concave penalty
• A Tutorial on MM Algorithms
• Ideal spatial adaptation by wavelet shrinkage

Cited by

• Enhanced Cyclic Coordinate Descent Methods for Elastic Net Penalized Linear Models
• Signaling of salience and prediction errors by anterior insula neurons
• Sparse-Group Factor Analysis for High-Dimensional Time Series
• Efficient computation of high-dimensional penalized generalized linear mixed models by latent factor modeling of the random effects
• Variable Selection with Multiply-Imputed Datasets: Choosing Between Stacked and Grouped Methods
• Versatile Descent Algorithms for Group Regularization and Variable Selection in Generalized Linear Models
• Variable selection via knockoffs in missing data settings with categorical predictors
• Estimation and variable selection for generalized functional partially varying coefficient hybrid models
• Variable Selection in Functional Linear Cox Model

Related

• A Selective Review of Group Selection in High-Dimensional Models
• Collinear Groupwise Selection via Scaled Group Lasso
• The composite absolute penalties family for grouped and hierarchical variable selection
• The Group Lasso for Logistic Regression
• Selective inference using randomized group lasso estimators for general models