Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection

Patrick Breheny, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

393 Citations (Scopus)


A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP), have been demonstrated to have attractive theoretical properties, but model fitting is not a straightforward task, and the resulting solutions may be unstable. Here, we demonstrate the potential of coordinate descent algorithms for fitting these models, establishing theoretical convergence properties and demonstrating that they are significantly faster than competing approaches. In addition, we demonstrate the utility of convexity diagnostics to determine regions of the parameter space in which the objective function is locally convex, even though the penalty is not. Our simulation study and data examples indicate that nonconvex penalties like MCP and SCAD are worthwhile alternatives to the lasso in many applications. In particular, our numerical results suggest that MCP is the preferred approach among the three methods.
Original languageEnglish
Pages (from-to)232-253
Number of pages22
JournalAnnals of Applied Statistics
Issue number1
Publication statusPublished - 1 Mar 2011


  • Coordinate descent
  • Lasso
  • MCP
  • Optimization
  • Penalized regression
  • SCAD

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty

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