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

TL;DR

This paper develops efficient algorithms for nonconvex penalized regression models with grouped predictors, specifically extending group SCAD and MCP penalties, and compares their statistical performance through simulations and real data examples.

Contribution

It introduces stable, efficient algorithms for fitting nonconvex group penalties like SCAD and MCP in regression models, advancing variable group selection methods.

Findings

Group MCP and SCAD outperform group lasso in variable selection accuracy.

Algorithms demonstrate stability and computational efficiency.

Simulation and real data show improved model selection with nonconvex penalties.

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.