The Annals of Applied Statistics

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

Patrick Breheny and Jian Huang

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Stat. Volume 5, Number 1 (2011), 232-253.

Dates
First available: 21 March 2011

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1300715189

Digital Object Identifier
doi:10.1214/10-AOAS388

Zentralblatt MATH identifier
05906805

Mathematical Reviews number (MathSciNet)
MR2810396

Citation

Breheny, Patrick; Huang, Jian. Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. The Annals of Applied Statistics 5 (2011), no. 1, 232--253. doi:10.1214/10-AOAS388. http://projecteuclid.org/euclid.aoas/1300715189.


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