Abstract

We consider “one-at-a-time” coordinate-wise descent algorithms for\na class of convex optimization problems. An algorithm of this\nkind has been proposed for the L<sub>1</sub>-penalized\nregression (lasso) in the literature, but it seems to have been\nlargely ignored. Indeed, it seems that coordinate-wise\nalgorithms are not often used in convex optimization. We show\nthat this algorithm is very competitive with the well-known LARS\n(or homotopy) procedure in large lasso problems, and that it can\nbe applied to related methods such as the garotte and elastic\nnet. It turns out that coordinate-wise descent does not work in\nthe “fused lasso,” however, so we derive a generalized algorithm\nthat yields the solution in much less time that a standard\nconvex optimizer. Finally, we generalize the procedure to the\ntwo-dimensional fused lasso, and demonstrate its performance on\nsome image smoothing problems.

Keywords

Coordinate descentLasso (programming language)Elastic net regularizationSmoothingRegular polygonMathematicsMathematical optimizationAlgorithmConvex optimizationComputer scienceOptimization problemCoordinate systemArtificial intelligenceFeature selectionStatistics

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Year
2007
Type
article
Volume
1
Issue
2
Citations
1908
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Closed

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Jerome H. Friedman, Trevor Hastie, Holger Höfling et al. (2007). Pathwise coordinate optimization. The Annals of Applied Statistics , 1 (2) . https://doi.org/10.1214/07-aoas131

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DOI
10.1214/07-aoas131