Concave 1-norm group selection

Dingfeng Jiang, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)


Grouping structures arise naturally in many high-dimensional problems. Incorporation of such information can improve model fitting and variable selection. Existing group selection methods, such as the group Lasso, require correct membership. However, in practice it can be difficult to correctly specify group membership of all variables. Thus, it is important to develop group selection methods that are robust against group mis-specification. Also, it is desirable to select groups as well as individual variables in many applications. We propose a class of concave 1-norm group penalties that is robust to grouping structure and can perform bi-level selection. A coordinate descent algorithm is developed to calculate solutions of the proposed group selection method. Theoretical convergence of the algorithm is proved under certain regularity conditions. Comparison with other methods suggests the proposed method is the most robust approach under membership mis-specification. Simulation studies and real data application indicate that the 1-norm concave group selection approach achieves better control of false discovery rates. An R package grppenalty implementing the proposed method is available at CRAN.
Original languageEnglish
Pages (from-to)252-267
Number of pages16
Issue number2
Publication statusPublished - 29 Jul 2015
Externally publishedYes


  • Bi-level selection
  • Concave penalties
  • Coordinate descent
  • p >n problems
  • Sparse group Lasso

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Concave 1-norm group selection'. Together they form a unique fingerprint.

Cite this