Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors
This work addresses group selection in regression for statisticians and data scientists, but it is incremental as it extends existing nonconvex penalties to grouped settings with algorithmic improvements.
The paper tackles the problem of variable selection with grouped predictors by developing algorithms for nonconvex penalized regression models like group SCAD and MCP, showing stable and efficient fitting through simulations and real data comparisons.
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.