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

Patrick Breheny, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

139 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)173-187
Number of pages15
JournalStatistics and Computing
Issue number2
Publication statusPublished - 1 Jan 2013
Externally publishedYes


  • Descent algorithms
  • Group lasso
  • Optimization
  • Penalized regression

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

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