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Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection
Journal article   Open access   Peer reviewed

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

Patrick Breheny and Jian Huang
The annals of applied statistics, Vol.5(1), pp.232-253
04/14/2011
DOI: 10.1214/10-AOAS388
PMCID: PMC3212875
PMID: 22081779
url
https://doi.org/10.1214/10-AOAS388View
Published (Version of record) Open Access

Abstract

Annals of Applied Statistics 2011, Vol. 5, No. 1, 232-253 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.
Statistics - Applications

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